Heads up oop with a K that may be good

[villains_hero]

Villain ist 38/28/2,5, multitabling winning regular

$15/$30 Limit Holdem 4-handed

Hero opens in the SB with K[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img], BB calls.

Flop 6[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/heart.gif[/img]

Hero bets, BB calls.

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

I think BB would have raised any pair without a flushdraw on the flop. At this point i think she has a flushdraw, a K (possibly both) or something very strong that didnt need protection on the flop.

If I check here I expect hands without showdown value and monsters to bet. If I bet I expect monsters and draws without showdownvalue to raise. A King will probably call, but unfortunately Im not sure about all that. And I dont know what to do now. Any insight is very welcome.

Or should I better ask my friend RIO what this one is all about?