So this is mainly about loneliness? And coming to terms with singledom?
It's a hard stage of life you're at. Big changes anyway with DC growing up and needing you less plus menopause etc.
A parent's job is to bring up independent DC ready to function as adults in the world and this means dealing with the empty nest syndrome. Maybe you've been fast tracked into that a bit with the divorce and the week on/week off thing. I've got no experience of the empty nest thing myself, maybe you can find out what do others do to deal with it?
Your ex is not as strong as you so he's went out and got a replacement with the focus on looks it seems. Don't feel jealous of their inevitably dysfunctional relationship. He didn't suddenly change and not become abusive upon divorce.
Your illness sounds life changing which is a big thing for anyone to deal with. Is there a support group for the condition that you could attend, to help you through the shock of adjusting to your new situation?
I don't think you need to give up dating if you don't want to. Maybe take a break to adjust first, so you don't go getting together with the first person who'll have you without considering whether they're right for you. Being overweight definitely isn't a barrier to dating, beauty comes in many forms and people have different preferences.
Being unwell doesn't necessarily preclude you from the dating scene either. You're a person, not a disease. Nobody is perfect and there's always a "but", this is yours. That doesn't mean you can't be someone's ideal person and your "but" doesn't bother them. It might even be an early warning system for weeding out the total waste of space types. I mean, look who Ms Young Slim And Presumably Nice has ended up with!
If you want to do something about losing weight you can look into options for that. Obviously it's not going to be as easy as just doing some exercise, with your health concerns, but that doesn't mean you can't ever lose weight, there might be a way.
Maybe you should try find places to go so you're not stuck inside churning it all over in your head so much. Are you being treated for the depression too? Or do you just need to change your life to shake it off? Even if it's the latter, medication might be needed temporarily to give you the motivation to do make the changes.