Poor people have poor diets because unhealthy food is less expensive than healthy food.
Poor pregnant women eat crap and feed their children crap, because that's the only food in the house.
(on the whole, on the average)
Bananas, lettuce, carrots, most fruits and vegetables....pretty cheap. Most grains like rice and dried pasta- pretty cheap. You can make pretty healthy pastas- without creams and fats and cheeses- that are very tasty pretty easily and pretty cheaply. Even the really bad for you pastas with all that crap isn't that expensive to make. And the Italians don't eat a lot of pasta- you're not meant to eat a giant bowl with over half a pound of heavy/creamy/cheesy pastas like we do here. They'll eat a decent sized, but small portion as part of a larger meal. Chicken breast, ground beef, ground pork - also plenty cheap cuts of beef. And the gov't does give out WIC pretty easily to low income women with children.
I think the real problem is one of convenience. It's way more convenient to eat cheap fast food or open highly processed junk foods out of a box and eat them or open highly processed canned/frozen foods and throw them in a microwave for a few minutes and eat them than it is to grocery shop continually for fresh produce/meats and cook.
The only time I've spent a lot of money at grocery stores is when I'm buying certain high quality free range eggs or high quality steaks or high quality shellfish like lobster or jumbo shrimp or high quality imported italian product like parmigiano-reggiano cheeses- which can cost a damn small fortune.
But
most fresh produce and a lot of meat (bacon, ground pork, pork chop, chicken, ground beef, and many cuts of beef) are pretty damn affordable at most supermarkets.
A lot of the processed foods and crap aren't so cheap. Junk food is almost more pricey than the real food.
I think a big part of the problem here is the portion sizes and complete lack of exercising as well. They walk a lot in Europe. We don't do that so much here. Unless you live in New York City- you take a car everywhere.