The main problem with obesity isn't lack of food, it's lack of GOOD food.
As a mental exercise, next time you're in the grocery, compare pricing. Look at how much it costs to buy GOOD food - meat, vegetables, dairy, vitamin water, juices, healthy foods - then look at how much it costs to buy CRAP - chips, candy, sugars, pastries, sodas. Don't worry about "organic" - personally, I think that's a scam - just look at regular old "good" foods.
THAT, is why we're obese as a nation. We eat CRAP. Now, the flipside of that argument is, we as a nation could NEVER starve, simply because we have so much crap on the market. If we were truly a third-world nation, there wouldn't be doritos; there wouldn't be Coke and Pepsi; there wouldn't be ANYTHING on the shelves, and we'd be fighting for what we could produce on farms (THAT, by the way, would absolutely cure obesity!).
If we really cared about "the poor" with food stamps, we'd limit WHAT they could buy with them. NO ice cream; NO sodas; NO junk food. You can redeem food stamps for HEALTHY food - grains, dairy, beef, chicken, pork, seafood.
Better yet, we'd limit food stamps period - you get them for a max of 3 months, while you are actively looking for a J-O-B. End of 3 months? End of stamps. Period.