I'm totally missing the relationship between being poor and being obese. I just do not follow the link you're asserting. It seems like a big non sequitur.
I'd sort of think, that you, as an economist would go for more of a national tax on soda. Basic basic macro, subsidize what you want, and tax what you don't. You seem to not want soda and also want to punish food stamp users. A tax like that would be regressive, and seem to support your (as i understand them) twin goals.
Instead, you're advocating piling on regulation, making both government and commerce more difficult. I kind of think you're just trolling me, but i'm still willing to give the benefit of the doubt.
What exactly is the link between getting food stamps and being obese, and how dose resolving that alleged connection solve obesity in the united states?
edit
I see, after a careful reading, you're not asserting it would solve obesity. You're asserting that soda, if not subsidized would be consumed less, thus improving the situation.
I think you're underestimating people's willingness to use food stamps for other things and cash for soda. I think you're not really evaluating soda vs sugar and are sort of arbitrarily picking that one thing.
I think the costs of the regulations you're proposing would overshadow any effect on the 5% of 5% who's behavior actually changes.
But, ok, now i see, you're not trolling. You're moving the goalposts from soda to sugar - but ok, you're not crazy.