If you decide to stay with your partner, I think my advice can help.

First, communication is the basis of all your relationship and cornerstone.

Talk a lot, meet again, explain how harmful the overweight can be and that you will accept the commitment to him, whether it is to share new hobbies or activities, with respect, because the decision to change is from him.

Second understanding, IT IS NOT EASY TO GIVE THE FIRST STEP.
It is the most complicated of all, after him there is only evidence and dedication of you.

Third, LOVE. As @nomad-magus says, he has low self-esteem and a very poor self-image, do not make him feel worse, tell him that he is progressing, that he looks good, that he looks handsome, loves him and makes him feel loved.

Avoid situations of stress because anxiety is very bad company.

A hug from a chubby husband who decided to change.