I don't know what their proposal was, but replace "fat" with "unvaccinated" in your response and you'll see what they (likely) were getting at. The logic of "you must get vaccinated to protect the vaccinated" eludes me, since I thought the vaccinated are already protected from severe disease (though crucially not from infection or transmission) irrespective of anyone else's vaccination status.

Full disclosure: I'm overweight. 14kg down from where I was a year ago, with another 10kg or so to go. I'm baffled that NIH/CDC said literally nothing about this issue as it relates to COVID since the beginning of the pandemic. One would think 18+ months is a sufficient amount of time to lose at least some weight, and thereby reduce the risk.