Obesity is generally protective against osteoporosis and bone fracture. However, recent studies indicate that the influence of obesity on the skeleton is complex and can be detrimental. We evaluated the effects of a high‐fat, obesogenic diet on the femur and radius of 1100 mice (males and females) from the Large‐by‐Small advanced intercross line (F34 generation). At age 5 months, bone morphology was assessed by microCT and mechanical properties by three‐point bending. Mice raised on a high‐fat diet had modestly greater cortical area, bending stiffness, and strength. Size‐independent material properties were unaffected by a high‐fat diet, indicating that diet influenced bone quantity but not quality. Bone size and mechanical properties were strongly correlated with body mass. However, the increases in many bone traits per unit increase in body mass were less in high‐fat diet mice than low‐fat diet mice. Thus, although mice raised on a high‐fat diet have, on average, bigger and stronger bones than low‐fat‐fed mice, a high‐fat diet diminished the positive relationship between body mass and bone size and whole‐bone strength. The findings support the concept that there are diminishing benefits to skeletal health with increasing obesity. © 2019 American Society for Bone and Mineral Research.