This article contributes to the literature that studies the impact of food prices on food choices and obesity rates. While it is now well established that daily calories consumption in excess of dietary guidelines and the switch toward more sedentary lifestyles are key factors for the rise in obesity prevalence of American men and women after 1970, there is much less consensus about what caused eating habits of men and women to change over time. We analyze the impact of food prices on body weight in a dynamic setting where men and women have different preferences and choose between J food groups. We derive an analytical expression linking preference parameters, including the elasticity of substitution, to empirical estimates of price and cross-price elasticity of demand for the J food groups. One key takeaway from the calibration is that there is substantial preference heterogeneity between men and women. We find that most food groups are substitutes and thus an increase in food prices, perhaps due to a sin tax, does not always lead to body weight losses.