If she doesn't have the urge to lose weight (which is frankly her right if she is so inclined), it's not your problem. You have no need to modify your body just to suit her desire, just like she doesn't see the need to change her body for your desire either.
I’m not suggesting you break lease. I’m suggesting that your partner take on the entire current lease.
Right now you’re both in apartment A. He wants to move to apartment B, leaving you alone in apartment A.
I’m suggesting that you move to apartment B, leaving him alone in apartment A.
That way, he’s the one taking the financial risk, not you.
If she doesn't have the urge to lose weight (which is frankly her right if she is so inclined), it's not your problem. You have no need to modify your body just to suit her desire, just like she doesn't see the need to change her body for your desire either.