I bet and here's why:

Villian kills you with AA or AK-AJ. He would of course jam the pot with these. But if we check this, I see him betting with not only those hands but KK-God-knows-what. On a coordinated board he would be correct in doing so.

At that point, we're either calling down with a second-best hand or folding a better hand. How do we know?--that blows.

If we bet, we at least get some information on Villain before we seal our fate in this hand. If he just calls, he almost certainly doesn't have us beat.

If he happens to raise, that's not a bad thing either, which is also why I think our bet is important. His raise does something for us we can't do ourselves: protect our hand (which admittedly may not be as good once he raises, but eliminating players is important to our success). On this board I love the idea of facing the others with two bets.

For me, all this adds up to betting being the most positive expectation.