His betting was very small so he could very well have a weaker pair or even a weaker ace high type hand. I think in situations like this we need to weigh the benefits of raising vs calling the donk bets.

If he is a cally/wally type don't raise with air. However, you can call his bets down here and try and make a pair with your ace or king. In this situation we need to weigh the implied odds of you hitting that ace or king. If he is a calling station we can certainly squeeze value out of hitting our hand. Of course don't forget to take into account reverse implied odds, because when we do hit that ace or king against guys like this we want to get the money in when we beleive we are ahead, but sometimes he's already made the better hand.