I was watching a hand and had a thought, but wanted to get some other opinions on it.

Blinds 5k/10/10k ante
hero UTG Ah6h raise 21,000
villain HJ QsTh calls
BB defends w/ QhTs
-FLOP 6dAc6c p:78,000
BB check-folds
HERO check/calls
HJ bets 30,000

TURN Tc pot 138,000
HERO check/calls
VILLIAN bets 60,000

RIVER 4s pot 258,000
HERO checks with 445,000 remaining in stack
VILLIAN checks with 637,000 remaining in stack

My thought here is, can we lead out with a polarized bet, or if we bet here are we weighted too value heavy and won't get called by worst often enough for it to be a profitable play, and should we just check/call and let villain continue to bet and have this be more profitable in the long run?