In some sense, yes, because to get to extremely high weights, you need to consume extremely high amounts of food. Your stomach will grow, but I would imagine a person would struggle to eat enough carrots to weigh 500 pounds. Quick napkin math says some obese people eat 6700 calories a day. 50 calories is ~12 baby carrots. That's ~1608 baby carrots per day. If my math is right, that's about 67 one pound bags of baby carrots per day.
Carrots are probably an extreme example, but I think the point stands that to get that overweight on healthy food, both the volume of the food and the time required to eat it become astonishing. I don't even know if we can metabolize carrots fast enough to eat that many in a day without rupturing some part of your stomach.
> "Normal" cooked meals that were the staple of nutrition before the advent of fast food are almost absent from their diets.
I think this is a big part of it. Calorie dense food has always been around. The problem was that it was often difficult and/or expensive to make. How long would it take you to replicate a Big Mac combo meal, and how much would it cost? It takes a while, especially given grocery shopping, and it's probably not much cheaper. Likewise, I can go to the grocery store and buy a whole cheesecake for like $10.
Honestly, I think the best way to tackle it is not to outright ban the foods, but just add an excise tax. If we added a 10% tax to soft drinks, fries and pizza, it probably wouldn't make a huge difference to the average citizen's spending. It would be a 10% increase in your food budget if that's all you eat though. If you want to go crazy, add a program that lets you earn that back by doing healthy things, like riding a bike. We should probably do that anyways. If we want to reduce the amount of driving people do, paying them walk/bike places instead of driving isn't a bad system either.