I have a 13 week old puppy that does not know when he is full?

I have a 13 week old doxie puppy. I have had a gazillion dogs and puppies before and have NEVER run into anything like this. He will eat until his stomach is wider than he is long! I took him to the vet, (he is "congested" and on antibiotics right now also) and I asked him about his distended stomach, I just wanted to see if maybe it was something else and not that he eats too much. Old country vet said it is too much food. Thing that sucks is my other puppy (a 9mo old pit) is used to free feeding and now I have to play kibble nazi and just give the doxie a handful... run and feed the pit and then stand there to keep the doxie away from the pits food! UGHHHH. Have any of you run into this and is this something he will HOPEFULLY grow out of? BTW even if I only feed him in the am and give him a handful in the pm his stomach is still huge. Yes, he has been wormed so it isnt that... just dont know what it might be. NOT having a good time with this situation!!!!