The empirical evidence of a non-monotone relation between income and obesity is not well explained.We build a theoretical model combining income inequality and social comparisons to explain the link between income and obesity and study tax policy implications for fighting obesity. We assume that differences in food consumption patterns between poor and wealthy households partly reflect positionality, which is the concern for social status. Our key assumption is that positionality for low-calorie food consumption is positively related to a country's wealth. In this framework, body weight outcomes reflect competing income and positionality effects, yielding the following results. We explain the link between average obesity rates, and standards of living and suggest the existence of a Kuznets curve for obesity.For cross sections of the population, we explain the observed correlation between income and obesity, which is positive in poor countries, and negative rich countries. We find that increasing the relative cost of high-calorie food is less effective at decreasing the relative weight of poor individuals in rich countries than in poor countries.