Crate him. Its safer for him and you in the middle of the night with how small he is. I crated my boys until they were almost 6 months old. Use a crate, cover with a blanket, put a blanket in with him so he's warm, and feels safe. He should sleep through the night, but yes he'll cry at first, you'll have to ignore it and he'll stop. Its hard but worth it for your sanity!
