Live MTT hand for review

[Percula]

Live MTT, $225 buy-in, 50K prize pool (nice overlay at 177 players).

We are 8 handed, I am in the BB with ~4000, I have only played three hands in the hour or so since we started, one raise from the BB to take out 3 LP limps and showed KK, two raised MP with AA and took it down on the flop and showed the AAA, three was a slow played QQ from the BB and again I showed my hand. I like to show some big starting hands early to set a tight image to setup for more stealing later.

So here I sit in the BB with KQo and it is folded around to me. I have a LAG in the SB and a tight player in the BB. LAG has about ~6000 and the BB has about 4000. Blinds are 50/100. I am thinking this is a good place to play a pot with the SB or simply steal the blinds, or just out right have the best hand against two random hands. I raise to 150, SB folds (shocked me there LOL), and BB calls (opps trouble there). The flop come KT3, BB bets 600 in to a 350 pot, this screamed AK to me as I seen him overbet with it a couple of hands ago. I mini-raise to 1200 hopeful it smelled like AA or KK, BB makes a crying call. Turn is a brick and the BB checks to me...

Now I am thinking back to some of the conversation I have heard at the table, things like "BB is a good MTT player", "lots of final tables", "a tournament point leader", etc. So my thinking here is...

1) I am beat, but he feels weak. Otherwise he would have pushed to my mini-raise, or would have pushed on the turn.

2) That he is a good enough player to laydown TPTK against what looked like AA or a set playing with someone that has more or less the same number of chips as him.

3) Do I check behind to look like I am trapping, or do I bet out and if I do bet out how much to make him fold?

So how would you play this turn and maybe a river too?