200NL - Turn check or bet?

[Bramsterdam]

Everest Poker No-Limit Hold'em, $1.00/$2.00 (HH Converter by Kreatief)

<font color="blue">Reads: Villain isn't a regular and is a shortstack, so I'm almost certain that he's a fish.</font>

Button ($217.80)
SB ($239.25)
BB ($50.80)
MP2 ($202.00) (Hero)
MP3 ($284.40)
CO ($200.70)

Preflop: Hero is MP2 with J[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/heart.gif[/img]
<font color="#CC3333">Hero raises to $7.00</font>, <font color="#666666">4 folds</font>, BB calls $5.00,

Flop: 6[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/diamond.gif[/img] ( $15 )
BB checks, <font color="#CC3333">Hero bets $12.00</font>, BB calls $12.00,

Turn: 2[img]/images/graemlins/heart.gif[/img] ( $39 )
BB checks, Hero?

I believe his range weighted towards Kx/Ax type of hands. Do I bet to charge Ax, or do I check to take a free card against Kx (and fold to a river openshove?

~PSB behind btw