All data were publicly available from the NHANES 1999-2000 cycle. NHANES, a nationwide ongoing cross-sectional study in the United States, collected health and nutrition information among the noninstitutionalized population through interviews, physical examination and laboratory testing. More detailed information about study design and data collection of NHANES are published on the official website (16).

The NHANES 1999-2000 cycle had a total of 9965 subjects participated in. Considering cell division and metabolism occur exuberantly until the age of 25, the maximum of weight/BMI is more likely to appear after the age of 25 (17). All participants aged 85 years and older in NHANES were recorded as 85 years. Therefore, we included participants aged 25 to 84 years (n=4257) and excluded the participants who had missing data on telomere length (n=1108) or the indicators of weight range (n=697). We finally had 2918 eligible participants enrolled for analyses. National Center for Health Statistics Research Ethics Review Board has reviewed and approved the study, and written informed consent was obtained from all participants.

The maximum and minimum of weight and the corresponding age were recalled at the NHANES questionnaires. Participants more than 18 years old were asked to recall the maximum lifetime weight and the exact age, and participants more than 19 years old were asked to recall the minimum weight since age 18 and the exact age. The maximum (BMI_max, kg/m²) and minimum (BMI_min, kg/m²) of BMI were calculated as the corresponding weight (kg) divided by the square of height (m²). We calculated the maximum minus the minimum, generating weight range (kg) and BMI range (kg/m²). In addition, we calculated the time between the maximum and minimum values. Annual rate of weight (kg/year) and BMI range (kg/m2/year) were calculated by dividing the corresponding range by the time. All calculations took into account the direction in which the change occurred.

The details of the telomere length measurement were reported on the official website of NHANES (18, 19) and elsewhere previously (20). The peripheral blood samples were obtained from participants in the NHANES surveys. Measurement procedure started from the extraction and purification of deoxyribonucleic acid (DNA). Quantitative polymerase chain reaction (qPCR) was used to determine telomere length in the laboratory of Dr. Elizabeth Blackburn at the University of California, San Francisco. Telomere length was measured relative to standard reference DNA (T/S ratio) which came from the human diploid fibroblast cell line IMR90. Each sample was assayed on duplicate wells which were blinded to the investigators. Eight control DNA samples were set in each assay plate, which were applied to normalize between-run variability. Runs which had more than 4 control DNA values falling outside 2.5 standard deviations from the mean for all assay runs would be identified as potential outliers and excluded from further analysis (<6% of runs). Telomere length were presented as the T/S ratio finally.

Covariates were constitutive of demographic variables, anthropometric variables, lifestyle factors, and medical comorbidities. Information about demographic variables [age, sex, ethnicity, marital status education, and family income-poverty ratio (PIR)], lifestyle factors (smoking status and alcohol use), and medical comorbidities [baseline history of diabetes, hypertension, cardiovascular disease (CVD), chronic obstructive pulmonary disease (COPD), and cancer] were collected by means of questionnaires. The anthropometric variables (baseline height and weight) were acquired via physical examination.

Among them, continuous variables included age (year), weight (kg), height (m), and BMI (kg/m²). Categorical variables included sex (male and female), ethnicity (non-Hispanic white, non-Hispanic black, Mexican American, and other), marital status (married/living with partner, widowed/divorced/separated, and never married), education (more than high school, less than high school, and high school), PIR (low income, medium income, and high income), baseline BMI (underweight, normal weight, overweight, and obesity), smoking status(never, former, and now), alcohol use (never, mild, moderate, heavy, and never), and baseline history of diabetes, hypertension, cardiovascular disease, chronic obstructive pulmonary disease, and cancer. Detailed explanation for covariate acquisition process is available on the official website of NHANES.

Participants with telomere length values and the indicators of weight range (BMI_max, BMI_min, weight range, BMI range, and annual rate of weight and BMI range) are retained. Outliers were handled by means of interquartile range (IQR), defined as values which were more than 1.5 times the IQR from the boundary of IQR (21). The lower outliers were replaced by the 25th percentile minus 1.5 times the IQR, and the higher were replaced by the 75th percentile plus 1.5 times the IQR. For missing of other covariates, we used multiple multivariate imputations to maximize statistical power and minimize bias caused by data excluded from analyses (22).

For continuous variables, we performed normality test by means of the Kolmogorov-Smirnov normality test. Mean ± standard deviation was used to describe normally distributed continuous variables, while median (Q1, Q3) to non-normally distributed continuous variables. Categorical variables were presented as frequency (n) and proportion (%). Among different telomere length groups (quartile), the one-way analysis of variance in normally distributed continuous variables, the Kruskal-Wallis test in non-normally distributed continuous variables and the chi-square test in categorical variables were performed to test the statistical differences. A boxplot was used to illustrate the distribution of telomere length according to the BMI range (deciles).

To investigate whether weight range are correlated with telomere length, univariate and multivariate linear regression models were employed. Four models were constructed to adjust for confounding effects of different covariates. Model 1: no covariates were adjusted. Model 2: adjusted for age, sex, and ethnicity. Model 3: adjusted for covariates in Model 2 plus educational level, family PIR, alcohol use, and smoking status. Model 4: adjusted for covariates in Model 3 plus medical comorbidities, including diabetes, hypertension, CVD, COPD, and cancer. Furthermore, we investigated the possible non-linear relationship between the weight range and telomere length by non-parametrically restricted cubic splines (23).

To test the robustness of the results, sensitivity analysis was performed by removing participants with any missing values and running the same statistical analysis. Subgroup analyses were performed through univariate and multivariate linear regression models in Model 1 and Model 4. We calculated the associations in different subgroups, including age (<60 or ≥60 years), sex (male or female), race/ethnicity (non-Hispanic white, non-Hispanic black, Mexican American, or other), smoking status (never, former, or now), alcohol use (never, mild, moderate, heavy, or never).

All data were statistically analyzed by R software (version 4.2.1). We considered that a two tailed P value of less than 0.05 to be statistically significant.

Data of 2918 eligible participants were ultimately included in the study and analyzed statistically. The circumstantial flowchart was displayed in Figure S1 ( Additional File 1 ). The telomere length among the final participants ranged from 0.389 to 1.626 T/S ratio, with a median (Q1, Q3) of 0.960 (0.805, 1.134) T/S ratio. The summary of general characteristics categorized by telomere length groups (quartile) was provided in Table 1 . According to the result of normality test, continuous variables in the study were non-normally distributed. Compared with those with longer telomere length, the participants with shorter telomere length tended to be older, male, Mexican American, and widowed/divorced/separated; besides, worse economic conditions, lower educational levels, and more comorbidities often accompanied them. According to the results of self-reported information, the median (Q1, Q3) age at least weight and greatest weight were 18 (18, 23) and 41 (30, 56) years. The median (Q1, Q3) of least weight and greatest weight were 58.97 (52.16, 68.04) and 81.65 (71.21, 96.16) kg respectively. An interesting finding, the inverse association between age at greatest weight and telomere length, exist in Table 1 , but it did not remain after adjusting for the covariates in Models 2-4 ( Table S1 ; Additional File 1 ).

As we demonstrated in the boxplot, the distribution of telomere length differed significantly for participants with different BMI range (P < 0.0001); and the BMI range between 0.572 and 3.562 had the largest telomere length ( Figure 1 ). This led us to explore the association between weight range and telomere length.

Presented in Table 2 were the results of univariate and multivariate linear regression regarding the association between weight range and telomere length. Model 1 was univariate and unadjusted for covariates. BMI_max, BMI range, and weight range were negatively associated with telomere length. However, annual rate of BMI/weight range exhibited a positive association with telomere length. There was no significant association between telomere length and BMImin. In the multivariate linear regression, indicators of weight range were respectively brought into the Model 2-4. After the potential confounders were adjusted for, the inverse associations persisted in BMI_max [β=-0.003, 95% confidence interval (CI): -0.004 to -0.001, P<0.001], BMI range (β=-0.002, 95% CI: -0.003 to -0.001, P=0.003), and weight range (β=-0.001, 95% CI: -0.001 to 0.000, P=0.001). Furthermore, annual rate of BMI range (β=-0.026, 95% CI: -0.046 to -0.007, P=0.009) and weight range (β=-0.010, 95% CI: -0.017 to -0.003, P=0.007) also presented negative associations with telomere length, after adjusting for covariates in Model 2-4. The association between BMI_min (β=-0.002, 95% CI: -0.004 to 0.001, P=0.237) and telomere length still could not reach statistical significance in multivariate linear regression model.

To address for nonlinearity, we also used non-parametrically restricted cubic splines analyses to visualize the association of weight range with telomere length. As shown in Figure 2 , the nonlinear inverse associations were observed in BMI_max (P for nonlinear =0.026), BMI range (P for nonlinear =0.022), weight range (P for nonlinear =0.035), annual rate of BMI range (P for nonlinear =0.030), and annual rate of weight range (P for nonlinear =0.027) after adjusting for potential confounders. According to the Figure 2A , telomere length reached the maximum around BMI_max of 24.9 kg/m², then started to decrease with increasing BMI_max. The plots in Figures 2C–F showed that longer telomere length existed within the lower weight fluctuation. And telomere length remained relatively flat during the changing of BMI_min ( Figure 2B ).

As shown in Table S2 ( Additional File 1 ), two methods of missing values treatment had the same trend. Univariate and multivariate linear regression analyses revealed that inverse association between weight range and telomere length remained but less significant in complete cases analysis.

Based on age, sex, ethnicity, smoking status, alcohol use, subgroup analyses were conducted in Model 1 and Model 4. For BMI_max, the inverse association with telomere length was still significant in both genders and different age groups. Those Non-Hispanic Blacks, Non-Hispanic Whites, never smokers, moderate and heavy drinkers also showed significant negative associations with telomere length ( Table S3 ; Additional File 1 ). The negative association between BMI_min and telomere length still could not reach statistical significance in any subgroups ( Table S4 ; Additional File 1 ). BMI range correlated negatively with telomere length in male; while the inverse association of weight range with telomere length existed in both genders. For participants who were younger (<60 years), never smoked and drank moderate amounts of alcohol, BMI range and weight range had inverse associations with telomere length ( Tables S5, 6 ; Additional File 1 ). The inverse association of annual rate of BMI/weight range with telomere length still statistically significance in male, the younger, former smokers and drinkers ( Tables S7, 8 ; Additional File 1 ).