Q on turn, likely has me beat, so hero...?

[StevieG]

Live at Flamingo last weekend, 2/4 limit. Table has been loose passive, but a raise preflop can shake some players.

I open raise with KJo in middle position, folded to the button, a calling station old lady who calls. Blinds come along.

Flop is J high with two diamonds. Checked to me, and the button (of course) calls, small blind drops, big blind calls.

Turn is a Q (not diamond) and the big blind bets out. Undercards to the QJ on the board do not help a straight. I know the old lady will call with straight draws and even payoff with busted draws on the river. I do not have a solid read on the big blind at this point, but I have not seen him raise anyone to this point, and I strongly believe he has the queen.

Hero....?