Poor people become obese because cost of food does not depend on calories, or rather is inversely related to calories. The cheapest foods tend to be the most processed, less nutricious, but very calorie laden.
So it's not exactly that they "still earn enough money" to become obese, it's that somehow the food supply has been inverted so everyone can afford calories but not so many can afford healthy food.
Besides that, as a counter argument to your hypothesis, wouldn't inner city neighborhoods be old and walkable? In that case, your argument that they are more healthy because they are inhabited by richer people doesn't seem to fly.
While this is true in general, it is still possible to eat a balanced, healthy diet for very little money. That said, it requires a lot of discipline and a somewhat sophisticated understanding of nutrition. Still, my wife and I managed to get by on $20-30/week for combined groceries for about a year (we're in AZ, and being vegetarian helps keep costs down), but still managed to eat well.
eru nailed it. We lived off bulk everything -- oatmeal, rice, beans. For fresh food, we got cheap veggies with lots of nutrition; greens tend to be the best bang for the buck, but also bags of carrots, beets, and such. For protein, it was all about tofu, eggs, milk, yogurt and nuts (mostly peanuts, soy nuts or pepitas, which are much cheaper than tree nuts). For beverages, bulk tea is absolutely the way to go, at just a few cents per cup.
Food prices have really shot up since 2006 though; in particular, bulk beans have almost doubled. Still, I think it would be possible to eat the same diet today for around $35/week for a couple.
Some cheap and healthy things: Oat meal, beans, tea / water, fruits of the season, yoghurt, rice, pasta, potatoes, sweet potatoes, cabbage.
I can easily imagine eating for around 2 Euro a day or even less. It just would not be as much fun. So I get around with 5 to 7 Euro, that allows me to add delicious ham and some other meat to my diet in small portions.
Characterizing the problem as one of "just laziness" is intellectual laziness. For one thing, the environment is dramatically different. People have an easier time sticking to rice and beans when that's pretty much all there is. In America, unhealthy food is not only more accessable but heavily marketed. You can't expect people to make similar descisions on average in such different circumstances.
If poor people are eating unhealthy food because of marketing it is still laziness. Take the time to find out what's good for you, it's not hard.
My point is that no one can honestly say that they are fat because they can't afford good food. There are tons of excuses, but it comes down to personal responsibility.
I'm not talking about excuses, I'm talking about your expectations. You're holding people born in America to a higher standard of discipline than those born elsewhere, and poor Americans to a higher standard than rich Americans.
Laziness? Is that based on opinion or data? This is an unbiased question. I am further interested in how widespread this sentiment is.
I heard a story about a McDonald's closing in a poor area. There are at least two effects of this, the second of which was quite surprising: 1. McD, a source of high-fat food, leaves the area, and subsequently people need to find alternative food; 2. McD, a source of cheap food, leaves the area, and subsequently people have trouble affording food.
Apparently McD's distribution chain is so efficient, that their presence resulted in wider access to food. I say nothing about nutrition, jobs, or anything else. Just food that fills your stomach. It seems like nothing is that simple enough to summarize in a single sentence. Doing so is likely overestimating of your grasp of the situation. But perhaps it is indeed just laziness.
I don't know of a study that makes the claim, but I can go to the grocery store and buy really cheap food that's not bad for me. It takes more work to prepare than hitting a preset on the microwave or going to a drive-thru, but it's cheap and will keep you healthy.
(I say this as I'm about to re-heat some left over spanish rice that I made last night. It cost almost nothing to make.)
I recently learned the great utility of beans and I asked why they aren't pouring over the streets. Apparently: culture, agriculture, and subsidies. A culmination of broken links.
So it's not exactly that they "still earn enough money" to become obese, it's that somehow the food supply has been inverted so everyone can afford calories but not so many can afford healthy food.
Besides that, as a counter argument to your hypothesis, wouldn't inner city neighborhoods be old and walkable? In that case, your argument that they are more healthy because they are inhabited by richer people doesn't seem to fly.