@vivify saidI think it's both.
Alabama and Mississippi also have the two lowest vaccination rates:
https://www.newsweek.com/these-5-states-have-lowest-vaccination-rates-highest-covid-cases-1615708
You've proven you know how to make sound arguments; so blaming their high Covid death rates on "obesity" seems like a deliberate attempt to mislead.
But between an obese vaccinated person and a healthy unvaccinated person of the same age, I'm not sure who had the better chance of severe COVID (I would imagine the obese person).