The guy who played Sam in game of thrones said he would ask people, who pointed out tye similar plot hole with his character, something along the lines of “you know I don’t actually live on the wall right?” I don’t want to search for the clip to find the exact quote so sorry if that’s too far off.
Also something along “theres living dead, giants, dragons, magic, and the only thing you find unrealistic is someone not losing weight?”
Becauae there is no in-fiction reason why that would be the case. Dragons aren’t realistic, but not losing weight is internally inconsistent with the rules of the world as presented to us.

John Snow regularly gices his best buddy his extra rolls because he has a gluten allergy.

Boom, explained.

I don’t have any context to know if that works here or not, but either way relying on headcanon to explain the primary text is a hallmark of sloppy writing.
And it would be good if they showed something like that on screen. Shows Jon as a kind friend, if a little too soft.
He was fat in the original books.