My son is the almost the same age yours and he is breast fed. He doesn't drink a whole lot at one time either. He has just started to sleep through the night and notice that he is eating LOTS through out the day. What you could try instead of waiting till he is really hungry, feed him a little more often. Try every hour in the evening before bed if he is usually every 2 hr. I am finding that my ds will drink more through out the day and now I make it a point to feed him more often in the evening so when he is finally a sleep for the night (between 10 and 11pm) he is out till anywhere between 4:30 and 6am) I feed him again and he will sleep for about another 3 hours. It is pretty nice.....now if only I can figure out a way to get the 3 yr old to sleep alittle longer.

Our babies are also almost ready for rice cearal, that is another option. I don't have ds on it yet because he is very content with the breast but when I had dd she wasn't as easy. I started her on cereal about this time and it made a world of difference for us. Some say it didn't for them but every baby is different. I hope this helps.
Sava