{{{hugs hun}}}
At 5 weeks feeding 3 hourly at night really isn't unusual. even as full term babies both mine did that. There are a few growth spurts in these early weeks so it can often feed like they are feeding all the time. the fact he is able to go 3 hours consistently through the day is fab too. Mine barely made it to 3 hours at 5 weeks.
I think your paed needs to give you a bit more support. One of the benefits of BFing is taht is pretty impossible to overfeed and should be reassuring you that what your LO is doing is totally normal BFing for these early weeks.
I think if you got the cluster feeding and DF consistent you may very well find you get a better stretch in the night. But be kind to yourself, it is very very early days. He is doing great as his weight gain shows! Well done you.
On the windy side...again i think this is normal for early weeks as they get used to eating and digesting and the rest. That could be contributing to him bringing back up some milk as opposed to over feeding. How is you let down? Sometimes a fast let down can lead to them getting windy? Is he draining the breast at a feed? Are you single side feeding?
HTH xx