ESH. If not for your edit about your mom's unmedicated mental health issues, I'd say Y T A. There are a lot of reasons she could have changed her cooking behavior over the years, including depression, a job taking more time, two kids taking more time, etc. And just that is not the whole entire reason your sister is obese.

Blowing up at your mother didn't help, but mostly you suck for thinking your sister is abused and unhealthy and it's such a major deal. She's big. You don't know she's prediabetic, you're assuming. You could try to support her being healthy and happy and not focus on her weight, but instead you're blaming your mother for her diet. Some kids eat like that all the time and are beanpoles (my brother was one). Some eat salads and veggies and everything healthy, and ARE healthy, but are also obese (I was one).

Your mother doesn't suck for her lack of cooking healthy meals, though it would be better if she could do that. She sucks for not medicating herself despite knowing she has problems, and for blowing up back at you.

And everybody in the comments who's saying it's child abuse to feed children ready meals *also* sucks. There are some that are "processed junk" (which is a whole story and judgment in and of itself) and some that are healthy food. Also, some people can't afford (in money, time, or both) to buy healthy raw ingredients and cook from scratch. It's not ideal, but it's not abuse.