Non-communicable diseases like diabetes, obesity and certain forms of cancer have been 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 global epidemics. Here, we implement a spatial spreading analysis to investigate whether diabetes, obesity and cancer show spatial correlations revealing the effect of collective and global factors acting above individual choices. We adapt a theoretical framework for critical physical systems displaying collective behavior to decipher the laws of spatial spreading of diseases. 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. This collective behavior indicates that the spreading dynamics of obesity, diabetes and some forms of cancer like lung cancer are analogous to a critical point of fluctuations, just as a physical system in a second-order phase transition. According to this notion, individual interactions and habits may have negligible influence in shaping the global patterns of spreading. Thus, obesity turns out to be a global problem where local details are of little importance. Interestingly, we find the same critical fluctuations in obesity and diabetes, and in the activities of economic sectors associated with food production such as supermarkets, food and beverage stores--- which cluster in a different universality class than other generic sectors of the economy. These results motivate future interventions to investigate the causality of this relation providing guidance for the implementation of preventive health policies.