Obesity is caused exclusively by calorie surplus. You can literally eat pure sugar, twinkies, and sugary beverages exclusively at base metabolism maintenance calories and never become obese.
As for your ignorant assumptions, I've been homeless for short periods of time in my life (in between jobs moving to a different city) and lived far below the poverty line for like 8 years of my adult life. Frankly, you have no idea what you're talking about. You can eat far healthier than the average american on the lowest budgets in the US. At literally half the poverty line if you spend 30% of your budget on food that's $5 a day on food - now you've probably never been poor so you don't understand how far $5 can take you in america - here's a nice showcase of what you can eat for $3.33/day
https://stackyourdollars.com/eat-on-5-a-day/
that's bacon/eggs/toast for breakfast beef burritos for lunch chicken and vegetables for dinner
and that meat you're spending money on can all be replaced by far cheaper healthier alternatives like lentils or beans
So again, you've got no idea what you're talking about
yet another $5/day menu that includes snacks, with mostly healthy foods and surpasses most peoples calorie needs https://uhs.berkeley.edu/sites/default/files/sos-eatingwell5...
I could do this all day, honestly as it's not even remotely hard to eat very healthy and very well on $5/day