Elevated body mass index (BMI) is associated with increased multi-morbidity and mortality. The investigation of the relationship between BMI and brain organization has the potential to provide new insights relevant to clinical and policy strategies for weight control. Here, we quantified the association between increasing BMI and the functional organization of resting-state brain networks in a sample of 496 healthy individuals that were studied as part of the Human Connectome Project. We demonstrated that higher BMI was associated with changes in the functional connectivity of the default-mode network (DMN), central executive network (CEN), sensorimotor network (SMN), visual network (VN), and their constituent modules. In siblings discordant for obesity, we showed that person-specific factors contributing to obesity are linked to reduced cohesiveness of the sensory networks (SMN and VN). We conclude that higher BMI is associated with widespread alterations in brain networks that balance sensory-driven (SMN, VN) and internally guided (DMN, CEN) states which may augment sensory-driven behavior leading to overeating and subsequent weight gain. Our results provide a neurobiological context for understanding the association between BMI and brain functional organization while accounting for familial and person-specific influences.