PurposeWe aimed to investigate the associations between parental BMI and offspring BMI trajectories and to explore whether the parent-offspring BMI growth trajectory association differed according to family SEP or social mobility. MethodsWe used data from the Avon Longitudinal Study of Parents and Children (ALSPAC). Children’s weight and height were collected from 1 to 18 years. Parents’ height and weight were reported pre-pregnancy. We assessed family SEP by measuring parents’ and grandparents’ educational attainment, social class, and social mobility by changes in education attainment across generations. Multilevel models were used to develop trajectories and assess patterns of change in offspring BMI, to associate parental BMI with these trajectories, and explore whether these associations differed by family SEP and social mobility. Results13,612 children were included in the analyses. The average BMI of offspring whose parents were overweight or obese was higher throughout childhood and adolescence, compared to those with parents of normal BMI. Parental and grandparental low SEP were associated with higher child BMI, but there was little evidence of modification of parent-offspring associations. For example, at age 15 years the predicted mean BMI difference between children of overweight or obese mothers versus normal-weight mothers was 12.5 % (95 %CI: 10.1 % to 14.7 %) and 12.2 % (95 %CI: 10.3 % to 13.7 %) for high and low grandparental SEP, respectively. DiscussionThese findings strengthen the evidence that higher parental BMI and lower family SEP were associated with higher offspring BMI, but we did not observe strong evidence that family SEP modifies the parental-offspring BMI association.