As others have said, communication is key. Although what he has said in regards to your weight, it's harsh, yes, but we all do have our preferences. I also do believe that couples should do their best to look after themselves for one another, even when children happen we should do our best to please one another - this goes for him too.
Maybe you two can join a class or work out at home together, be more active with one another doing different tasks to start getting close again. Also, dress up, get your hair done and buy yourself something new and both of you go out and enjoy yourselves. We can fall so easily in to routine that we do forget ourselves, but you two seem to still care about one another so it's time to put the effort in.
The success of this relationship relies on you both, he has told you his concern, if you have any you need to voice them too. Your children are no longer that young where you need to be constantly chasing after them, it's time you both went back and revisit how you fell in love and start over.
Keep communicating, start working on building your confidence again, your man does love you - now you need to start loving you more and get the best out of you. You both will be fine if you keep being honest and communicate.
I'm wishing you both so much happiness, I hope this is a new start for you both and that your children can witness their parents being cringe and soppy over one another. You will get there, you know what you need to do - it's now time to act. Best wishes to you both!