Pressing forward with a marginal hand....

[private joker]

I play this the same. On the river a check is the right thing to do -- your kicker doesn't even play anymore, so even 53o is chopping with you. But any better 5 that's been calling (A5, K5s -- a hand it seems this table would play) beats you, as does a 4 that wants to check-raise, or 77/A8/98 that's been playing passively. I don't think a worse hand calls a river bet as often as a better hand does. And no better hand is folding, obviously.