Sounds a lot like our household when I was younger. I was always overweight, and I was pretty badly bullied because of it. My brother, however, was always way too thin because he exercised a lot. For me it always helped a lot to do a diet together with my mom. We would both go to the gym together and eat the same healthy dinner while my dad and brother would get high calorie options. This way I did not feel alone in being hungry and it made me a bit competative too (wanting to lose more weight than my mum)

I think the best you could do is have a careful talk with her. tell her that you are a bit worried about her eating habits and ask if she would like to try and eat healthier. Ask her if there are any sports she would want to try. Maybe make her eat keto dinner but let her eat bread/crackers for breakfast and at school. My mom used to hide the unhealthy food for me but tell my brother where it was.. made me a bit mad but yeah it was helpful :) She sometimes bought chocolate and sneakily gave that to my brother to put in his room. For herself and me she would buy really dark chocolate that I could have, so I did not mind too much. good luck!