one month weight check confusion

I just had my (or my lo's) one month appointment. He was born three weeks early and was only 6lbs 1oz, then was down to 5lbs 8oz at his one week appointment, even though his head circumference and length are average. At this appointment he was up 6lbs 12oz, which means he gained well over a pound in three weeks, which I think is great. However because he is still skinny they still want me to give him extra calories. I'm conflicted about this because he has gained steadily, he just had a low starting point, and honestly I don't know if I could possibly feed him more than I do (he feeds on demand and when I can I give him an extra bottle of either pumped milk or formula). What do you think-should I feed him more or continue what I've been doing?