I would say dont make the mistake your sister made. The kid said no.
You could say to her, “I know you didnt like what X said. I want to respect your boundaries. but if you ever WANT help with any sort of health issue, you can ask me, and I will respect you.”
then leave her be.
So I’ll just throw this in there. I’m trying to lose weight myself and every time one of my family members tries to take control of my diet/life because “they care about me” it makes me want to eat a “fuck you” sundae.
This is probably at least partially stemming from a lack of autonomy in her personal life so if your actions interfere with that it’ll probably make it worse
All you really can do is talk to your parents about managing food in the house, but not in like a targeted way, in a general way. Also invite your sister out on physical activities, but keep it small nothing strenuous or she’ll feel worse. Try walking around the neighborhood and catching up, or going to a park for a walk. Make it not about her weight but about you two together.
Your parents should also encourage her to see a therapist and address her eating disorder. But that’s up to your parents not you.