Playing AK offsuit with 6 A 6 flop and 1/2 stack raise from villain

[urnodaisy]

I am a beginner just starting out. I just got pushed out of a qualifier tournament at Party Poker on this hand:

10 player table I have AK offsuit blinds 600/1200 50 ante two hours into the tournament q at our table is about 9K I have 13K. EP calls and I open from MP1 3XBB every one else folds except EP(stack 16K) who calls. 2d position folds so I'm heads up with EP from MP1 and I'm last to act.

Flop comes 6d Ad 6c

EP raises 5K, I go all in with my two pair aces and sixes. EP calls.

Turn is 6s. River is 10s. I get full house sixes and aces EP has four of a kind (has a pocket six and had trips at the flop) and wins. I'm out of the qualifier like that.

When EP bet 5K should I have assumed she had trips or had my 2 pair beat and folded? Or should I have called or was my raise ok or should I have raised less? At the table she seemed pretty conservative although showing down A-x a lot at the ten person table and her betting was to raise preflop and then check and fold often to large bet or raise.

Is two pair heads up aces and sixes too weak a hand to go all in on when I'm heads up like that?

That was aggravating. I think maybe I should have called. But if I had called and seen that third 6 at the turn I would have had a full house and probably still would have gone all in prior to the river card. Could I have gotten away from this hand?? Should I just have assumed that the 5K was too much to call with aces and sixes against a conservative player when its almost half my stack? Should I have raised more than 3x the big blind to begin with? With the high blinds and my M of about 9-10 didn't I need to make a move or should I have folded and waited?

Thank you in advance for your help. Fossilman and Gigabet are you out there? Please help.