Way ahead/Way behind?

[AtticusFinch]

My line worked out well here, but I have this nagging feeling I played this hand poorly.

$11 PS MTT, blinds at 25/50. I'm sitting on 3k. Folded to me on the button, I raise to 150 with ATo. BB, who has me covered, pauses for 15 seconds then calls.

Flop is AKQr. Villain, a tight but semi-tricky player, checks. I smell a rat and check behind.

Question 1: Would you have bet here?

Turn is a blank. Villain minbets 50. Now I really smell a rat and just call.

River is a ten. Villain minbets 50 again.

Question 2: Your action here?

I raised half the pot and villain pushed.

Question 3: Call?

Results in white.

<font color="white"> I called and opp turned over KQ. How the hell could I be so sure he didn't have a jack, or a set? Was this just a good read or plain foolhardy?</font>