Hand vs. cts, draw + showdown value

[Requin]

I never know what to do in this kind of spot (the turn). I usually like check/calling, but have been advised that betting again is much better against a good opponent. Thoughts on both turn and river appreciated. Sorry for the mess but converter's down.

***** Hand History for Game 5192163533 *****
$600 NL Texas Hold'em - Sunday, September 17, 18:00:31 ET 2006
Table Monster #1277198 (No DP) (Real Money)
Seat 6 is the button
Total number of players : 6
Seat 6: cts ( $2664.49 )
Seat 3: LeRequin_ ( $847.05 )
Seat 2: jasonmathis ( $186.49 )
Seat 1: julick1 ( $554.06 )
Seat 5: s4508 ( $614.75 )
Seat 4: U2PLAY ( $304.67 )
julick1 posts small blind [$3].
jasonmathis posts big blind [$6].
** Dealing down cards **
Dealt to LeRequin_ [ Jc Tc ]
LeRequin_ raises [$24].
U2PLAY folds.
cts calls [$24].
julick1 folds.
jasonmathis folds.
** Dealing Flop ** [ 6c, 2h, Jd ]
LeRequin_ bets [$45].
cts calls [$45].
** Dealing Turn ** [ Qc ]
LeRequin_ checks.
cts bets [$126].
LeRequin_ calls [$126].
** Dealing River ** [ 2s ]
LeRequin_ checks.
cts bets [$386].
LeRequin_?

edited for his SN even though I'm sure everyone knows it...