My niece was born at 36 weeks and weighed 3.9 lbs. She is now 2 months and BIL told me last night that she weighs 8 lbs. I am happy that she is doing good and gaining weight, but is that to much.
With preemies and IUGR babies (which I am thinking your neice may have been if she was under 4 lbs at 36 weeks), there's no such thing as too much weight gain in the early months! My son was 3.2 lbs at birth and had doubled that by the time he was 2 months old.
They want preemies to double their birth weight early, and ideally they would like to see them double what a term baby would weigh (7ish lbs) by 6 months if possible. My son was born at 4 lbs 6 ounces, and was 10 lbs even by 2 months. My doctor was thrilled because he has caught up to full term babies - which is a good thing, not a bad thing.
Re: When did your lo double their weight