I think it sounds as though he may need his hay rationed. Maybe try him with 1lb or so divided between two feeds, night and morning. That may still be too much - I don't know how big Babydolls are, I didn't even know we had any over here - so you may have to cut back further.
Like all herbivores, they do need to keep eating to keep their guts active. So twice a day feeds are a minimum. If you can supply it in a way that takes him time to eat, or spread it over more, smaller feeds, so much the better.
Ideally you would not keep a sheep on his own, no. But you say he is able to see and talk to his pals? And isn't behaving as though distressed?
It's a bit like having a laminitic pony, I guess.
Alternative tactics would be sending him to somewhere with little, poor grass. But what to do for companionship... He isn't actually ill, so unlike a laminitic pony where getting better trumps company...