I hate to say it, but correlation is not causation. Unless you can provide some studies that show people who get rich e.g. from lottery winnings, also lose their weight and vice versa with proper controls for depression and the like there is no reason to believe that an increase in economic inequality will lead to an increase in obesity.
The lottery winner sample is a bad one because the argument about poverty causing poor health behavior is an overall lifestyle problem and not just a resource one.
Children who grow in the upper middle class or upper class will grow up with access and encouragement to participate in physical activities, parents who are better informed and able to construct healthier eating habits and the resources and cultural permission to use mental health professionals as needed.
Winning a 100 million jackpot after growing up poor can't change that.
