I'm not going to put myself through something I don't enjoy unless I can see it helping me to achieve something I do enjoy.

This right here. It's all about time preference. Delayed gratification.
Your larger friend has lived like there's no tomorrow, for too many tomorrows.
Completely fine if she's willing to own it; but not so cool if she wants to try and dump responsibility on a smorgasbord of others.

Personally I don't claim to struggle with my weight. I'm too comfortable with it, that's the problem. Struggling would burn calories.