Button versus BB ITM live, bet into on turn with draws

[betgo]

$2K live MTT, 31 players left, 40 places pay. Average stack 110K. More big stacks at this table, but a lot of people hanging on with tiny stacks.

My image is tight from play at this table, where I have been since the bubble burst. However, that is not my reputation from people who have played with me earlier. Story has been told about how I got old guy now 2 to my right to fold KK face up on J63r flop in 100/200 level.

SB is stevejpa with about 130K. I have 81K and BB has about the same. BB seems fairly tight. Blinds 2000/4000/400.

I open raise on the button to 11K with Kh7h. BB flat calls. Flop comes 8h6c4c and goes check/check. Turn is a Qh for 8h6c4cQh. BB bets 20K. What should I do? Any comments on preflop or flop?