Never ending diaper change at night

This is what it feels like to me. My baby is currently 4 weeks old and breastfed. He wakes up 2-3 hours to feed. Sometimes 4 hours. We feed first, wait a few minutes then change the diaper. A lot of times, I change him first so he’s awake to nurse properly. But the problem is that he poops after every breastfeeding session because he’s gassy or has stomach cramps. For example, I woke him up at 3 to nurse, changed his diaper after he pooped. He was wide awake then I nursed him to go back to bed. Then he pooped again (smaller quantity). Nursed him again and he pooped. This is about to be our 3rd diaper tonight also meaning I’ve been awake since 3am. It’s past 6 now. According to those I’ve asked, it’s normal for bf babies to poop after nursing but is it really ? Will it stop? I don’t want to wake him to change his diaper because he also must be tired 😩