As a number of people have responded to you, the issue, while simple, is not what you're stating. That's something that can be adjusted for and overcome pretty easily.
The real issue is that more developed nations have found methods of mass-producing cheap consumables -- cheap to produce, cheap to buy, lacking in nutrients, rich in other stuff that causes obesity (or sometimes just the wrong balance for your body to process as "working" food). These consumables have replaced grown vegetables in the diet of people with less income, because they're more easily affordable at the time they're needed.
Ron Finley spells it out pretty clearly. When his poorer neighbourhood converted abandoned lots and street easements into places to plant edible food, obesity levels dropped, vandalism dropped, and most importantly, diabetes levels dropped.
It's correlation and not causation, but this is a pretty damning result suggesting that convenience "foods" are a major contributor to the obesity issue (likely because of what they use as fillers, preservatives and growth hormones).