significantly decreased stamina isn't particularly advantageous when one attempts to lead a consistently athletic lifestyle.
And it’s already been said that (a) there’s no reason to assume that every character had led a consistently athletic lifestyle before the adventure starts, (b) that even with the amount of exercise that would be expected of a fighter or barbarian, they could still be fat, and (c) if we are going to assume that our character being fat (or thin) impacts their abilities then we can reflect that in their physical stats - whereas at the moment we could have an 8 Str, Dex and Con human male wizard who looks like he works out consistently.
So, from my perspective, there’s nothing intrinsically unrealistic about allowing some of the custom characters we create to be fat, even if we did agree that such a character (on average) would find physical exertion more challenging than an (average) character with lower BMI.
Regarding words, obese as you say has a technical meaning and it’s possible to be significantly fatter than the existing human female model, for example, without being obese. “Fat” is more general and seems to be the preferred term these days, having been somewhat reclaimed from those playground bullies, so let’s go with that for the purposes of this discussion.
