Last 4 tables, 30 players left avg. stack 110k blinds 2000/4000 my stack: 18bb

So the big stack opens, I did not have a large enough sample on the hud but his vpip was about 22% or so. he was the most active player at the table, and this happens:

http://www.boomplayer.com/nl/poker-hands/Boom/16211350_5F824069B4

My thoughts:
I decided to call the minraise, protecting my BB. I check/call the flop thinking he might have an ace with higher kicker. then the 9 comes and I make 2 pair, and decided to put in a small bet, making my hand look weak and hoping for an AJ-AK to reraise. He just called. I'm still thinking about aj-ak (/maby qq / kk / jj). Now im betting 95% of my remaining stack, to make it look like a bluff still hopinh he calls me off with Aj-Ak.

Could i do anything better? check turn/river maby? but what if he does bet out after my check, can i lay down after the turn?

Just wondering what you guys think :)