Your citations show a link between poverty and obesity, not gluttony. If welfare programs were generous poor people might be able to afford fresh vegetables and other nutritious foods less linked with health issues, rather than the cheap, high-calorie, low-nutrition foods.
Obesity is a direct product of gluttony (i.e. eating more than you need). If the poor were really financially constrained, they would eat a smaller quantity of high caloric density foods.
(There is one exception to this - tall muscular people. This is a known problem with BMI.)
It's also a product of low exercise (common if you're scraping by with two minimum-wage jobs), depression (common when you're poor), eating (cheap) junk food instead of fruits and vegetables, etc.
Low exercise doesn't cause obesity. Low exercise combined with high caloric intake does. I.e., eating more than you need.
I successfully maintain a healthy bodyweight through periods of low exercise (typically resulting from injury). Right now I put in the effort to eat 4500 (reasonably clean) cals/day. When I'm unable to train, I cut it to 3000.
People suffering depression may choose gluttony at a rate higher than others, but that doesn't mean depression causes obesity. Gluttony does.
If a person were truly financially constrained, they couldn't engage in gluttony if they wanted to.
I'm aware that one can be obese and have scurvy or something along those lines.
From what I've read, the primary diet-related medical problems that the poor suffer are diabetes, heart disease, and similar things. Scurvy and B12 deficiency are very far down on their list of problems.
Feel free to do a google search and prove me wrong.
