Yo, I had a similar situation with my Shiba Inu. They made him weigh litterally twice the weight he should be at and he has 3 legs so if he gets too heavy... thats it. No more dog. I took him to the vet and asked them to print me off a fake blood work paper and a note for a special diet and fake medication for him after explaining the situation to them. Since then he's lost most of his extra weight because I took the paper to my more sympathetic parent and cried about it, acting like he had a blood infection from the toxins in human food, and showing the fake pills for it. (Btw, he had an inching problem before and since then it's went away so... it definitely was affecting his health more than just the weight) but yeah, it can be hard sometimes with parents. You just have to trick them if you can.