[AdamBragar]

I think checking down is probably the best option here.

The only place I can see a value bet is on the river. My guess is SB would have bet if he had anyhting substantial on one of the streets. This did not happen, so I'd guess that SB has a lower pocket or QQ or made a loose call with KQ or KJ.

My only other thought is betting maybe half the pot on the river as a value bet hoping JJ, 99, 77, 66 calls you. But this is even risky, cause a lot of the time, players with those hands will fold pretty quickly to any bet and players with other hands will raise you as well as players that find your half the pot bet weak.

Nothing wrong with checking and hoping to see the pot go your way.