[ilya]

I think your most likely holding is a weak hand that stands some chance of being good if the hand is checked down on the river, but is too weak to bet. I don't think you're on a total bluff as you checked the river and you can't be at all sure that villain will bet. The one strong hand I could see you having is a rivered two pair, as with a flopped set/two pair you probably bet out on the flop or turn, and you either check-raise or bet out on the turn with a turned two pair. Checking 2 pair on that turn in a 6-way medium-sized pot seems like asking for a suckout. Sooooo....if you do have a strong hand, I think it's most likely A7/Q7/J7, probably without a flush draw.
I can't really see you checking those hands on the river too often, though. Although it seems like there are many draws he may have missed and will now likely bluff with, I think his preflop raise and flop check narrow the possibilities a lot. He doesn't figure to have a ten unless it's AT or TT, and he probably bets the flop or checks again on the turn with the former, and checks the turn again with the latter. He doesn't figure to have a club draw unless it's with KcQc, and there's no likely holding that gives him a heart draw. His most likely holding IMO is a marginal made hand like KK or KQ. It's a little strange that he would bet the river with either of those hands, but he may well figure that you would have raised with the various Aces either preflop or on the turn, and that your big stack will encourage you to make a loose call with a Queen or a Jack.

So yeah. I think you call the turn with a hand like JT or QT thinking you are likely beat, but have outs & a chance to bluff your opponent out on the river. On the river you check because you think he'll call a moderate bet with holdings like KK/KQ, and don't want to risk a large bluff cos your hand is too good. When he bets, you know you're too likely to be beat to just call, but you figure you can make him fold a lot of hands as he hasn't shown that much interest in the pot & he has plenty stack to fold.