See this is one of those very rare moments when I actually feel vaguely thankful for my autism, because my life has been no better than Troll's life, but because I'm so emotionally crippled I don't feel nearly as bad about it. I mean granted if it weren't for the undiagnosed autism my life wouldn't have been so awful, so it's a bit of a catch 22. I guess I can say the autism has made me more capable of bearing the awful life that the autism has bestowed on me.
But seriously, your 'sociality is a muscle that you have to flex or it atrophies' bit is just some crybaby bullshit. I had a whole 'let me show you what a battle with depression is really like' rant planned, but I couldn't figure out a way to say it without sounding condescending and that wasn't the attitude I wanted to convey. Let's just say that I empathize pretty directly with most of your problems, but mine go all the way back to at least first grade, and I never let my weight go quite as bad as you did although I do currently weigh the most I ever have in my life. I actually found a therapist that I liked and who knew how to talk to me without running me off, but I stopped seeing him because I find it hard to care about my problems, even though that lack of caring is going to lead me to suicide at best, and far darker things at worst.
I know you're not likely to listen to some dude on some random forums, but man just get out there and start getting rejected. As long as you don't go all fetal after your first rejection and go back to hiding in a cave, rejection is better than loneliness. You may not realize it, but it's not that hard for even an overweight mentally ill dude to end up in a relationship. Even if that relationship turns out to be a trainwreck, which it probably will, a trainwreck is better than no relationship at all, and maybe in the middle of all those trainwrecks you find something actually decent. Hell, even if you NEVER have anything beyond a chain of trainwreck relationships, I guarantee that will be better for your mental health than hiding in a cave like a troll.