Sorry for the format here, this was a hand I played on Global and HHs are kind of a pain over there.

25c/50c table with 6 players. No significant reads.

Hero is dealt KcJdTd7d in the SB. UTG through BTN limps. I complete because it seems pretty obvious, no? BB checks.

Flop 9c8h3d. I decide to check my wrap, having no blockers to pair/two-pair/set continues and a zillion opponents still in. Everyone checks.

Turn 2c. I bet half-pot with a lack of certainty; UTG, HJ, and BTN call. Weak, sticky ranges, I guess.

River Ts. I figure I want to keep my many opponents' bluffs and value-cuts in their river "VPIP" ranges, so I decide to check/call.

As played, UTG checks, HJ bets (a size I'll leave out for now), BTN folds. Hero?

So, multi-part question:

Would you prefer to bet/fold this river or check/call?

How does sizing play into it for you? Is there a size that you don't check/call? (Is there a size you check/raise?)