Obesity prevalence is increasing in many countries at alarming levels. A difficulty in the conception of policies to reverse these trends is the identification of the drivers behind the obesity epidemics. Here, we implement a spatial spreading analysis to investigate whether obesity shows spatial correlations, revealing the effect of collective and global factors acting above individual choices. We find a regularity in the spatial fluctuations of their prevalence revealed by a pattern of scale-free long-range correlations. The fluctuations are anomalous, deviating in a fundamental way from the weaker correlations found in the underlying population distribution indicating the presence of collective behavior, i.e., individual habits may have negligible influence in shaping the patterns of spreading. Interestingly, we find the same scale-free correlations in economic activities associated with food production. These results motivate future interventions to investigate the causality of this relation providing guidance for the implementation of preventive health policies.