20/40 Live. Getting tricky with AA

[PGarlic]

20/40NL at Lucky Chances, 4 handed. I (~$2500) open on the button for 120, BB(~$1600) reraises to 340, I call. BB is stuck over 10K and has been playing agressively. He's come over the top of my button raise once before and has been auto raising on the button. He's an aggressive player in general though and likes to play a lot of hands. His biggest leak IMO is that he has a hard time laying down. I've seen him call off a lot of money with hands like bottom pair.

Flop: K 7 7 (suits irrevelant)

BB checks to me! That check really threw me for a loop. I thought he would bet regardless of the flop. At that point I put him on either AK or a PP lower then a K. With AK, he thinks he may think he has me drawing slim and wants to wait till the turn to get the money in.With a PP he may want to observe my bet, deciding then if I have a K or not.

Anyway, in my mind I have the nuts( unless he has KK) so I check behind, planning to bet the turn if checked to again.

Turn: K 7 7 9

BB then fires out 400. I'm not sure if BB thinks he has the best hand with something like AK or thinks he needs to push me off of a PP lower then a K. I decide to just call the bet, maybe re-raising all in here is the better choice?

River: K 7 7 9 8

BB immediately shoves the rest in, I think for a few seconds then call. What do you guys think?