Alright $1/$2 home game. Pretty serious game. We are 8 handed at this point and the pot I am talking about involves me and one other player. Here is some history on the other player...

Very tight pre-flop and then gets aggressive post-flop. Knows the game well but will take a gamble and check something big with a flush or straight draw out their. He is known for making his enourmous re-raises with big hands like AA, KK, and QQ. However I have layed down AK to him pre-flop to him after he re-popped huge only for him to turn over AQ. That hand was actually mentioned a bit earlier.

So to the action. All folds to me.

I make it $12 to go two from the button with As Ks. He looks down and pops it up to $30 from the button. I think and really want to lay it down because I know if I miss I lose a big pot and if I hit I still might have to lay it down. I decide to see a flop and hope for a good flop.

Flop---Qh Kc 3d

I didnt like this flop. I check into him and then he checks right behind. Now I'm thinking its either AA, QQ, JJ, or maybe he tried to pull something on me again wiht AQ.

Next card is a low brick and I decide to check into him again (dumb). He makes it $50. I think and fold.

He claims to have had JJ but I'm not too sold.

What mistakes did I make here and what would you do?