Certain things are glamourized in this world. Saying we should include fat characters in our generally idealized stories is basically saying we as a society should shift the set of things we glamorize so that it makes a minority feel better.
Atm, what we as a society glamorize is mostly depends on what the masses like, and what companies try to propagate to forward their brands and ventures.
IMO, ideally, you should train people to recognize these societal glorifications for what they are, which is just things to be enjoyed, not reflections of the truth. You shouldn't advocate for a different set of glorifications in order to lull fat people to thinking the reality is some how kinder for it. The reality is what it is.
I think there was a line of criticism against LN's for glorifying being living an otaku lifestyle. If there was a parallel universe where such otaku-glorifiying LN's didn't exist (that was like 15 years ago), that would be fine, too. I'm sure there were and are a lot of otaku who felt pressure (both external, from people's opinions, and internal, from lack of validation) from the type of lifestyle they chose/fell into.
The main issue with fat people is not the difference of preference (that should very much be allowed), but existing prejudice. Fat people shouldn't be bullied in school, or insulted anywhere. But those are difficult challenges that revolve around human nature. If your fat and some asshole insults you based on that, that's because they are an asshole, and not particularly because you are fat. Or they have a prejudice. The prejudice, and more importantly, how people act on that prejudice, is the more productive and realistic issue to tackle.