Instead of looking strictly at how much he drinks per feeding, you should be looking at overall daily intake, and also his weight gain. Is he gaining weight appropriately, according to the growth charts in his peds office?
Also, how does he seem after his 2-3 oz feeds....does he seem content and full? His stomach is still small, so I wouldn't worry about the small, frequent feeds. That's still normal. A breastfed baby at this age would be drinking the equivalent of what your son is drinking, and at the same intervals.
Small stomachs mean smaller, more frequent feedings. He digests his feeds quickly, since he is drinking 2-3 oz at a time. I also would not expect him to be able to sleep through the night yet. He needs those night feeds for growth still.
Trying to force him to drink more at his feedings would potentially lead to reflux, and an overdistended stomach, which could make him irritable, as well as start to make him vomit up some of the feeding.
Think of it this way: you and I eat until we're full. We have larger stomach capacities, so we can eat more food, but at wider intervals. His stomach is about the size of a tangerine/small apple, and holds less than what we can eat in one sitting. Would you like it if you were made to eat more food after you felt full? He's the same way. Just be patient - he will start to eat more when his stomach can hold more, and when he goes through growth spurts.
Good luck!