We use data from the National Longitudinal Study of Adolescent to Adult Health to investigate whether the quality of tertiary education -measured by college selectivity- causally affects obesity prevalence in the medium run (by age 24-34) and in the longer run (about 10 years later). We use partial identification methods, which allow us, while relying on weak assumptions, to overcome the potential endogeneity of college selectivity as well as the potential violation of the stable unit treatment value assumption due to students interacting with each other, and to obtain informative identification regions for the average treatment effect of college selectivity on obesity. We find that attending a more selective college causally reduces obesity, both in the medium and in the longer run. We provide evidence that the mechanisms through which the impact of college selectivity on obesity operates include an increase in income, a reduction in physical inactivity and in the consumption of fast food and sweetened drinks.