[FourKing Hell]

Hand 1. Your post:

Bet = weak hand, because he likes to checkraise.

Check = strong hand, because he would have bet if he was weak.

My extrapolation:

2nd check.. I take it you put your opponent on JJ-KK or perhaps 99 (high raising standards). That does fit in with the betting the flop because he's sort of weak part.
But you didn't bet the turn, because you were afraid he might have a good hand after all, that you hoped you'd bust him with (he won't pay off with a pair KK or lower if you hit).
Yet on the river you decided he was weak again, and bet.

Why not bet the turn? Granted, you lose the opportunity to double up vs. TT and possibly AA. But if he plays as you described, he'd check AA on the flop, leaving only TT to worry about. Did you at all consider the possibility that he was stealing, or had something like KQ?

Given that you DIDN'T bet the turn, I would consider checking behind on the river. If he was stealing, there are some hands you can beat outright. If he wasn't, you have to consider the possibility that he might call you down anyway, because you first called, then checked behind and didnt fire until he checked for the second time. He might even have AJ. I like your bluff after he showed weakness, however, given that your opponent is a notorious checkraiser AND you actually have a pair to show down, you might be better off saving your bluffs for when you totally miss.