Help!!! Weight gain?

Emma

I have a 6 week old son that is barely up to birth weight. We have been doing weekly weight checks and as of last Friday, he was only 8lbs 13 oz (8lb 15oz at birth).

Here’s what I know:

-eats every 2-4 hours even through the night

-latch is good

-supply is good (I pump approx 7oz each time I pump)

-when he’s at the breast, he either stops feeding or falls asleep and is satisfied. Relaxed, open hands etc.

-pediatrician has been having us bottle feed every other feeding and he usually eats 4oz from the bottle

-all his weighed feeds, he takes in 3+oz of breast milk.

-has plenty of wet and poopy diapers.

But he’s still not gaining weight very fast. I don’t know what to do. Per the pediatrician recommendation, I have given him 1 bottle of formula per day the last week and he spits over half it up every time. So the last few days I’ve been pumping and feeding breast milk with bottles and he does better with those but is still not gaining quickly. He’s gained maybe 2.5 oz since his last weight check.

I have noticed his poops are really stringy? They seem to be the right color but it looks almost like snot is mixed in. (See pic)

Anyone have any ideas??? I have been working with his pediatrician since birth and they are so great at reassuring me, but I just can’t help but feel that something more is wrong...