The underlying assumption to all of this is that poor people are disproportionately obese. I'm not sure that's as clean-cut as the assumption assumes. There might even be some subtle racial/class bias underlying those assumptions. Maybe rich white people see that movie with Precious carrying around a bucket of fried chicken and they think most poor people eat like that.
According to this, obesity rates tended to increase with decreased income only for white women. Black and Mexican-American men and women, and white men, experienced higher BMI’s with higher incomes.
Relationship Between Poverty and Overweight or Obesity « Food Research & Action Center