First of all I would not be considering whether villain is thinking about my range given that I raised the flop i.e. therefore I cannot have KJ. Players like this are thinking about there own hands only most of the time.

I would say bet bigger on the turn and still value bet thin on the river. I usually find a fold here as I have to see some concrete evidence that a player is capable of check raise bluffing rivers before I come close making hero calls in these spots.

Another serious consideration though is whether he is new to the game or unaware of hand strengths and betting worse for value.

However, the game flow, table dynamics and timing should be taken into consideration. You said you had been raising his bets a few times before, how had he reacted? Is he only playing one table? If so then he probably would have noticed that you had been aggressive with him a number of times before. With regard to timing there is the timing of his initial check and the eventual raise which should be taken into consideration and his timing overall. By the latter i mean this; sometimes I find that when i have been beating up on one player (usually to my right) they take longer and longer to fold each time I bet or raise and they can eventually start playing back at me. Generally this is only applicable if the player is playing one or two tables.