Common mechanisms in aging and obesity are hypothesized to increase susceptibility to neurodegeneration, however, direct evidence in support of this hypothesis is lacking. We therefore performed a cross-sectional analysis of magnetic resonance image-based brain structure on a population-based cohort of healthy adults. Study participants were originally part of the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) and included 527 individuals aged 20-87 years. Cortical reconstruction techniques were used to generate measures of whole-brain cerebral white-matter volume, cortical thickness, and surface area. Results indicated that cerebral white-matter volume in overweight and obese individuals was associated with a greater degree of atrophy, with maximal effects in middle-age corresponding to an estimated increase of brain age of 10 years. There were no similar body mass index-related changes in cortical parameters. This study suggests that at a population level, obesity may increase the risk of neurodegeneration.