Tough Decision with marginal Two Pair

[JammyDodga]

Hi, I'm afraid the site I play on doesnt provide hand histories, so you'll have to make do with my description.

200 Player $10 MTT,
30 players left, 20-30th pays $15, 10-20th pays $18, 9th pays $40, then goes up steep after that.

Blinds 400-800

Action is folded around to Button with 20k who flat calls.
I'm in the SB and call with K[img]/images/graemlins/diamond.gif[/img]6[img]/images/graemlins/diamond.gif[/img] I have 8k
BB Checks (has 7k)

Flop A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/heart.gif[/img]

I check, BB Checks, Button Checks.

Turn 6[img]/images/graemlins/club.gif[/img]

I bet Pot (2400)

BB Folds, Button goes all in. To call would cost me just under 5 k for a pot of 12k

What should I have done?

I'm thinking I played this badly, I should have either bet around 1600 on the turn and folded to a re-raise all in which would have given me the information I needed more cheaply, or if I planning to get them all in, check call so I could extract some value from hands i did have beat like A rag or a busted straight/flush draw.