Hmmm, well need to seperate the arguments out. I think it is self evident, that fatness cannot be caused directly by poverty. Skinnyness, sure.

However, vitamin nutrition and obesity are not the same. Is there a possibility that someone could not get the USDA recommended vitamins/etc per day on a low budget? Possibly so, I cannot say authoritatively until I think that one through a little bit. But the simple answer to poverty/obesity is tied to stress. Eating is well documented mechanism for dealing with stress, and poverty also has a well documented correlation with lack of education.

In other words, it is perfectly logical that stressed out people who are frustrated and know little or nothing about dietary science, or simply dont care , could be readily tied to obesity. If it was high calorie food - eat half as much, simple answer.

Also, in regards to eating inexpensively but well - my personal recommendation is to examine what does happen to be inexpensive in your area, then cross reference it with ethnic dishes comprised of similar ingredients. In truth, most "ethnic" dishes came about because people with limited economic resources worked very hard at making what they did have more palatable. There is no one universal answer, but many clues can be found.

Personally, when I was working with less money in my own food budget the things I found invaluable were a rice cooker and a wok.

I will say part of the problem regarding actual nutrition, is how much nutrition has been bred out of many vegetables and leafy plants in favor of appearance and shelf life. But that is a different topic.

For who could be free when every other man's humour might domineer over him? - John Locke (2nd Treatise, sect 57)