No idea if this thread is still active but I am going through something almost identical and I will tell you the male perspective with out any sugar coating.
Firstly you don't have sex with him and you don't even sleep together and I would suggest to you that it is incredibly selfish for you expect your husband to be celibate.
So he's probably thinking what does he actually get out of the marriage for all the work he puts in and now that he is more established as a man he probably thinks he can do a lot better now than what he settled for with you all those years ago.
That is a very selfish way of thinking, probably triggered by the lack of sex, if you are over weight that probably doesn't help either, so he is feeling incredibly guilty about it, Even if he doesn't love you he will still have feelings for you and really doesn't want to hurt you or the children. He is also probably afraid of losing his kids as well.
So he is not a child that cannot make up its mind, he is being torn apart by these competing desires, but i understand this leaves you in an awkward position.
Depending on what you want to happen there are a number of things you can do.
1)Guilt, shame and threaten him into staying with you, he will never be happy but you will get what you want.
2)Fight for him and your marriage, go down the gym, be sexy, make him feel wanted and desired.
3)Let him have a fling, as long as he is discreet you can turn a blind eye to it and he will get what he needs from it. In all likelihood he is just looking for an ego boost.
4)Leave him.