As you baby was born 5 weeks prematurely I would say that you cannot compare his weight to that of a baby who was born at full term.
Babies are born weighing differently.
He has put on 1lb 11 ounces since he was born. So I would say that is a good thing and he is eating and drinking.
If you are concerned about his weight, I would suggest you speak with your doctor or midwife. But as he has gained weight since he was born and everything else is normal and he is healthy, I do not think you have anything to worry about.
Best wishes.
I just want to know how much should a baby weigh at 1 month old