Dunno to me there is no inherent connection in that it shames her for it to me.
I see it in the way that nothing would really change for me if you'd replace her model with any of the maincast girls. Which is the thing I liked about it. She's clearly comfortable in her skin. Which is always a good message.
Doesn't really matter that she serves the role of being the antagonistic punchline it would have worked the same if it was a different model. Which is basically why it did not evoke a "fat shaming" sentiment to me.
Is that really so out there of a view? Maybe others can comment.
I was a fat kid. Being seen as greedy for food and having my physical form shamed was a huge part of being bullied. These are exactly the notes they hit.
Moreover, being fat as a kid, it is assumed you don't know it. Her confidence is meant as comic relief. My assumed okayness with my body was comic relief.
This is how this shit works.
Edit:
I am a guy, so the running assumption was I was gay--so a lot of flashing, butt slapping that kind of thing. For fat girls I've known, it tends to be instead the assumption that they want to get with hot 'normal' guy x and don't realize how wrong that is because they are fat. Notice this is exactly what they make her be like. I got some of that with respect to girls, but not much. Again, it was mostly the assumption I was a fat, gay, nerd.
She is the embodiment of the fat girl as joke to not fat people in school and she aggressively pushes this on to the poor 'normal' girls and guys who push back.
Edit 2:
Moreover, when I grew tall and lost a lot of my round appearance, the reactions to me completely changed. Now I am generally reacted to positively by men and women. It is a whole different world, and the juxtaposition is fucking disturbing and depressing.