(There is one exception to this - tall muscular people. This is a known problem with BMI.)
It's also a product of low exercise (common if you're scraping by with two minimum-wage jobs), depression (common when you're poor), eating (cheap) junk food instead of fruits and vegetables, etc.
I successfully maintain a healthy bodyweight through periods of low exercise (typically resulting from injury). Right now I put in the effort to eat 4500 (reasonably clean) cals/day. When I'm unable to train, I cut it to 3000.
People suffering depression may choose gluttony at a rate higher than others, but that doesn't mean depression causes obesity. Gluttony does.
If a person were truly financially constrained, they couldn't engage in gluttony if they wanted to.
Are you saying that it's impossible to be malnourished and obese?
If so, that's provably untrue.
From what I've read, the primary diet-related medical problems that the poor suffer are diabetes, heart disease, and similar things. Scurvy and B12 deficiency are very far down on their list of problems.
Feel free to do a google search and prove me wrong.