Do we bet or check this turn?

[Master Macavity]

PokerStars 3/6 Hold'em (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Hero is Button with K[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/spade.gif[/img].
UTG calls, <font color="#666666">5 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 fold</font>, BB calls, UTG calls.

Flop: (6.33 SB) 4[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/club.gif[/img], 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, UTG checks, <font color="#CC3333">Hero bets</font>, BB calls, UTG calls.

Turn: (4.66 BB) 3[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, UTG checks, Hero ????




Normally I'd bet there in a heartbeat, but the more I think about this, the more I wonder if this should be a check.

Briefly IMO, arguments for betting :

Nut flush draw, gutshot straight and 2 overcards gives me a pretty strong hand. I have fold equity over high cards which may have called this far.

Arguments for checking :

I don't want to be check-raised without an actual hand, although I would have to call, I'd rather let someone else lead the river then raise if I hit. No idea about my opponents holdings, BB could have any 2, and utg may have either 2 high or a low pair which may have flopped a set.

Please forgive any formatting errors, I'm still learning how to use them on here!