I have the same, exact, issue. Kid is 3.5 months, get about 50% breastmilk (that's with pumping, domperidone, etc). I only bf her at night. SHe usually wakes up at 2, 4, 5.30, etc. I"m thinking I'm not giving her enough to stay asleep, but I hate the thought of breaking out the bottles and when she wakes up for the morning she IS happy. She will take more suppliment in the morning, though, showing she is running a bit of a deficit by that time.
What is bad is that I'm not getting enough sleep, so I usually sleep through the morning, being woken up by my husband at 10 to feed her, and then at 12 if I'm not up yet. I get barely any sleep at night (I'm also have terrible problems with insomnia!). I usually pump at midnight to get at least something for the next day. Occasionally if she's had a particularly large suppliment before bed she will not wake up at 1:30 or 2, but that's only happened a few times.
I've been experimenting lately with dropping all pumping so I have more milk for her in the middle of the night, but I'm not sure it is making a difference, and then I've lost that little bit of milk for supplimentation the next day. It's hard to figure out what to do! -j