First define "fat". That's a wide term from just a little overweight to morbidly obese.
Well, just to paint broadly (so don't get all upset with me), it is more often the poor who are "fat" because food is expensive, and good, healthy food is even more expensive. This isn't just fast food, but real food that you'd buy from the grocery store. Ever gone shopping? It's easy to run up a $200 bill. Also, the poor often work jobs that don't allow them time to exercise.
Now, to be fair so I don't get a herd of thumbs-downs, middle-class families are also often overweight, and in their case it's being either cheap at the grocery store or just not caring about getting exercise. Some people don't even care about being overweight (like my sister-in-law, as a perfect example).