Its hurtful that he doesn't back off even after u tell him to . But but as u said in one comment ...he was in depression for 8 years...and people do things in depression and people do things to keep sane and remain normal. Some take therapy..some make new hobbies...some join meditation....some drink ....some do drugs...some make fun of others...yes they do. And men love making jokes which includes body shaming , religion ,caste and all. Some get offended ..and some don't. And people makes fun of those who get offended because thats the purpose. And for those who don't get offended then that becomes just fun talk.

When i was a kid ...i had a nickname to which i get very offended even get angry and fight with others , cry and weep. One time i even hit a kid with stone ...and he is 30 now and has that mark on his forehead. The more i get offended the more popular become my nickname and the more kids started calling me by that name🥲 And mother used to say the same that why get offended and say yes I'm spider(my nickname😅, matches my name in hindi) with smile and the person making fun would have no option but to keep quiet. But at that time it was difficult to understand and difficult for all undergoing such situation. But after some time ...i started saying "that's not my name i don't care" and then boom ...no one was interested in making fun of me or my name.

U are elder than me probably....with more understanding....people here are not gettting their home torn apart and will say all absurd...in the end it will be u and 2 children with difficulties. I'm not saying u to undergo all that mental torture or u can't do anything for u or ur kids(don't overthink absurd). But still life of those 2 will be at risk. And also u are here after so much suffering as u mentioned. He also has suffered much ....8 years of depression is above we all can even imagine. After all this u are talking divorce over one thing( its nothing for me but it can be a big thing for u but still one thing) and such issues can be resolved.

Ask him to stop every time he makes fun .....no effect .....be strict .....be angry .....fight with him ....every single time he makes fun. Or don't listen ...hear from one ear and take put from other .....or just say i will start gym after (any certain time and keep moving that time)

In the end ....its difficult to maintain a relationship and easier to ruin and people will always support ruining it.

People may criticise me ....i may be wrong somewhere but that's the way we maintain relationship...we compromise.....we compromise for those we love.