NTA

I understand your concerns. It's hard to go through something so horrible and seeing history repeat itself in your younger sibling. You want to protect them from that pain by telling them what will happen, even if they won't listen.

But there are some things you simply can't get across until they experience it themselves. Either she will grow to accept it or she will have to understand is through pain (and hopefully without dying as result). Be there for her as much as you can, because one day if she finally admits it, at least you'll be there with experience and sound advice. Perhaps, in the meantime, you can help by having her participate in cooking and showing an alternative to junk food that your mom has been feeding her. It's not much, but at least it's better than doing what she accuses you of, which is fat shaming.