Hi, welcome
When you say he is tiny, how small is he? Was he a premmie? Any other medical issues going on? Just don't want to advise you something inappropriate.
To me, it looks like he needs to drop that catnap to get himself some longer more restorative naps in the day, something more like this:
6 am: Wake Up for the day
6 am: E- bf
715-730- E solids (maybe a BF after as a drink and to add more calories)
9-10:30 am: Nap
10:45 - e-bf
11:30-1145: E solids (maybe a BF after as a drink and to add more calories)
130-3 - Nap
315-330: E-BF
500: e- solids
600: bedtime routine/bath
645: e-bf
700: in the crib
I do wonder if he's snacking (not ever taking a full feed, just frequent little ones) and therefore not taking enough calories in during the day or if solids is replacing too much of his daytime milk intake (solids being lower in calories than BM) and he's hungry at night.
I think also you have a BF to sleep prop involved. I'd say a lot of these wakings will probably resolve with fixing that day routine up a bit, but you may need to think about if/how you plan to wean BF to sleep so both of you get some decent rest at night.