Check-raised on flop again

[Fiddler]

I raise KK UTG everyone folds until a 33/15/3.5/35 player 3-bets from SB, BB folds and I cap. SB check-raises me on an AJ8 (A and J same suit).

He seems to have some post flop aggression issues but he is also pretty tight with the raising pre-flop. So is he trying to drive me off a better hand, with a lower pocket pair or draw (I didn't have the king of the possible flush-draw) or is he overplaying a hand that has me crushed? This is the kind of stuff I want to have in my notes on a guy. Not this time though.

Call-down to show him I'm a showdown monkey for the future or peel and fold the turn if I don't improve and he keeps firing?