I think he will outgrow it. My son needed to nurse once a night around 3 am until he was closer to 15 months. For me, it was much easier to just get up and nurse him because both of us were up for about 5 minutes. A couple of times I tried to see if he could go without it since, like your son, he was big and my doctor said he didn't "need" it. I have no tolerance for letting kiddos cry, though, and, I'll tell you - he sure thought he needed to nurse. :-) I was worried it was going to go on forever, but he gave it up when he was ready. If it isn't making you exhausted, I'd say just keep giving him the bottle for awhile longer. There is no "right" answer - its just what will work best for your family.
Good luck,
B.
Mom to a baby and a preschooler