Poor obese people aren't working so much they don't have time to cook.

And using numbers to support that idea doesn't work, it actually goes against you. A small (much smaller than most obese people will eat in one sitting) fast food meal costs about an hour of minimum wage! Buying stable calories in cereals where the time to buy and cook them can be amortized into many more servings can be amortized is actually cheaper and also takes less time.

In the US, obesity rates rise as income drops, but it continues to rise beyond the point at which income drops below a full time federal minimum wage income.

It's over-eating and under-exercising. I know this is hard for certain ideologies to accept because it means obesity is not inflicted upon victims against their will and beyond their control. If you really need to minimize their agency and responsibility for their choices you can call it addiction to food and addiction to sedentary lifestyle if it helps.