I live in Appalachia, so I see it, too. But poverty is linked to obesity, due in part to food insecurity. It may seem counterintuitive. But in developed countries it is the case, particularly in the West. There are a myriad of reasons for it. Some of which you touched on.
Just regarding that part of your post:
My wife is big sister to a girl (12 yo) here who is living with her grandmother who is pretty helpless. Her mom is around but is currently getting surgery on her arms to reduce the effect of using them as pincushions. Interestingly, the girl has no weight issues. She's not very intelligent and very small for her age (due to how her mother took care of herself while pregnant) but she's at least trying to learn, she's a cute kid and she is very salvageable. She has her eyes wide open regarding her mom and her lifestyle.
There is another girl (15 YO) from our church that we tried to "take in" as a friend, but she is so obnoxious that it is making it difficult to even try to help her. She is fat, constantly hungry, and will not eat anything healthy we put in front of her. And no amount of encouragement or positive talk works on ANY subject. It's like talking to a bag of raw narcissism. She is utterly oblivious to any attempted teaching of any kind. It's like trying to talk rocket science to a two year old. We've decided to apply our efforts elsewhere.
The sad thing about the 15 year old is that she is a walking caricature of the multi-generation welfare recipient mentality. The idea of actually aspiring to earn your own living is so foreign to her that she can't grasp the concept. EVERYTHING is about how to simply "get stuff" from the government and other people. It permeates everything about her world. Here is just how derailed her family is:
She claims she was sexually abused multiple times several years ago by her mother's ex boyfriend. That man has re-entered the picture and he says he's really sorry and he's changed. He now lives in Texas. So, mom has decided to move to Texas with him, but she can't yet. So she wants this girl to move there first and live there for a couple months while mom gets things in order in KY before she moves. Seriously? Yes, seriously.
How do you fix that kind of stupid? And that is what it is. It is not ignorance. It is raw, unadulterated, in your face stupidity.
There is some very messed up stuff going on around here. It's like another species.
I've heard of the food insecurity issue, but not read much about it yet.