There is an interesting question in there from the OP though, as a long time ago poorer people were thinnner ( I was one of them) and never got enough to eat as a child really, always felt some hunger.
I do think it could be the type of food that people eat now, that is readily available as snacks that is causing the problem of obesity, and the amount of sugar consumed in drinks and chocolate.
Poorer people are always going to be at a disadvantage with food, as in the past it cost more ( the rise of supermarkets and basics ranges means that it's cheaper now) but at the same time parents are usually both working so have less time to make a meal that is both nutritious and healthy.
I don't believe anybody chooses to be obese, of any class, but that it just happens slowly.
I live in what could be called a very nice area, and the majority of teenagers are slim ( often very slim) that I see, but adults are a mixed bag, all kinds of sizes.