baby having small feeds in night

Katie
My baby is 2 months old. The last 3 nights he has been waking for his feed between half 12 and 3, but only drinking between 2 and 3 oz when he is on 6oz and drains the bottle during the day. I don't understand why he does it, but he has a couple of ounces then goes back to sleep until his next feed. Should I try him with some water as he may just be thirsty or shall I just give him the milk as normal? He has been lasting longer during the night going around 5 or sometimes 6 hours. When he does wake up he isn't crying he just lies there for a while and he does his own thing. I don't know if what I'm doing is right by getting him up and giving him the bottle.