Crying call on river or muck it?

This is a hand of minethis past weekend in a 10-handed 6/12 game at the Borgata. I'm doing it from memory too, so I may not get all the preflop 100% accurate, but it will be close.

Hero is in BB with 6 [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/club.gif[/img]

Preflop: UTG calls, UTG+1 calls, 4 folds, CO raises, Button cold calls 2 bets, SB folds, Hero calls, UTG, UTG+1 calls

Flop: (10.5 Small Bets) A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/spade.gif[/img]
Hero checks, UTG checks, UTG+1 checks, CO bets, Button calls, Hero raises, UTG calls, UTG+1 folds, CO 3-bets, Button folds, Hero caps, UTG folds, CO calls

I thought I would try to check raise to give flush draws poor drawing odds, but I realize that they were still getting at least 6-1 which leaves them in fine shape. Should I have waited until the turn to check raise?

Turn: (10.5 Big Bets) 3 [img]/images/graemlins/spade.gif[/img]
Hero bets, CO calls

River: (12.5 Big Bets) 8 [img]/images/graemlins/spade.gif[/img]
Hero bets, CO raises, Hero vomits in his mouth and....

I would think I am probably beaten, but would calling 1 more bet for a pot with 15.5 Big Bets in it be so horrible?