Most important, if the government would stop subsidizing corn and soybeans and start subsidizing fruits and vegetables, we could begin to make real progress.
I'll probably get a tractorload of snow dumped at the end of my driveway for saying this, but Lupien makes sense. Our agricultural market has been knocked out of whack by government intervention to favor agriculture products that don't really feed people. For instance, 80% of the corn we grow goes to feed livestock (which, yes, we do eventually eat, but imagine how much better that meat would be if the livestock ate grass!). Far too little of the corn we directly consume is fresh corn on the cob. More than three times as much corn is used to make high fructose corn syrup and other sweeteners than is used to produce cereal and other directly consumable corn products (see the chart on page 4 of "US Corn Growers: Producing Food AND Fuel" from the National Corn Growers Association).
Government subsidies of corn and beans drive producers away from healthier products. The result: the cheapest foods are indeed the least healthy. The seemingly paradoxical increase of obesity among the poor is a result of bad choices, not by the poor, who act quite rationally in choosing the cheapest foods, but by the government, which favors certain agricultural corporations who proceed to flood the market with cheap, fattening food.
Now I can't guarantee that the government could make everyone give up Cheetos in favor of celery sticks by an overhaul of its ag subsidies. But by shifting the market back toward fruits and vegetables, the government could drive some healthy changes, as the poor might find healthy food more affordable, and, as a not so peripheral benefit, many of my neighbors might find it more profitable to turn their cropland and their cattle back to pasture.