Playing a big pair when an ace flops

The other day in a NL tournament I raised three times the big blind (600) with KK, and got one caller. There was an ace on the flop, but I bet 1,000 anyway (the rest of my chips). My opponent had an ace and I was out.

I wondered for several days whether I'd made the right move by betting out on the flop even with the ace overcard, but my thinking was that if I just checked behind her, she'd be sure to pounce on the turn with anything and I'd never even know if my kings were good.

Last night on the PPT I saw Jennifer Harman do the same thing. She had raised preflop with JJ, an ace came on the flop and she bet anyway against a single opponent, taking down the pot. Her results were different than mine but the play was similar, except I believe she was first to act, whereas I was last to act.

How do you play a big pair when there's an overcard on the board, particularly against a single opponent? Do you think I should have checked and given up the pot if my opponent had bet on the turn? I tend to think I did the right thing, even though it ended up putting me out of the tournament. It's probably relevant, though, that I was up against the chip leader and perhaps I should have played more conservatively because of that.

If you've only got 1600 left pre-flop, I'd be more inclined just to push rather than making a standard raise.

By betting the flop on an Ace high board, you might be able to push them off a weak Ace, conveying your preflop raise as a standard AK/AQ move.

As it happens, if I was the chip leader and caught any part of the flop, I'd be calling your all-in too. Just an unlucky board.

Yeah, I thought about that after the fact, too -- that perhaps I should have just pushed all-in preflop -- but I'd been playing really tight and wanted a little action with my kings. Oh well, another day....