[andyfox]

"Since the river card could make a better two pair"

Seems to me there's no way David can put him on a better two pair.

Actually, it's hard to put poster on any hand here. But I would think by checking again, David might think poster would take a shot here with a lot of hands and that poster would know that David would know this, and thus be apt to call a check-raise from David with a bunch of hands other than air.