I probably would of bet the flop first off, about 19,000 maybe, I doubt he would be only calling you with AK,  and since you have QQ, I doubt he has something like KQs.  If you check it all the way down, then your not getting much value out of your hand.  If you bet the turn and he only calls, I would still put in a value bet on the river, (1/3 pot) to get him to call you with a medium pp. 

Interesting situation:

Slightly disagree with the guys in that I really like you checking back the flop.

As you were the PF aggressor I think he's highly likely to ck / raise the flop. I reckon that he bets the turn if he's ahead but I still don't mind your check.

bjizz makes a good point regarding a possible villian bluff but the way the hand played out I think he's played it terrible if he has you beat.

I'm betting half pot and calling his shove.

Got 2 option on the flop (easy):

C-bet and rep the K – if he check/raises then oh well

Check back which is fine

Depending on what u do depends on what u should do on the turn:

by now the pot will be around 77k, if you bet. You would have around 47k. Enough to shove the turn, but if called on the flop  I am not shoving.

If he bets into you on the turn, imo u gotta fold. 47k is enough for a reshove stack just sucks u had to lose chips with QQ.

If he checks back to you on the turn:

I would check again. I mean if you bet you are gettin called for the most part by better hands. You can probably get TT or JJ to call but ill save this instance for the river.

In this case on the river:

He checks twice, looks like he has no K, he is just waitin and prayin for a showdown. You can bet and get weaker hands like 99, TT or JJ to call just b/c of how weak you played it.

Also though checking is not so bad. You leave all his possibles out there, whereas betting decreases the amount of weaker hands he will show you.

Alot of this depends on how the player plays. If he is the type of guy that will check to you with a better hand waiting for you to name the price then I would be cautious. However, if he isnt this crafty you can fire a bet on the flop (c-bet) or river (look like you want the pot).

I don't mind checking the flop since you made it so huge preflop.  I'd probably make it like 16.5k, but I would bet turn once he checks again and check back river if he calls turn.  As played bet river.