[Pokey]

It's hard to decide if BB missed his check-raise on the flop or if he woke up with a hand on the turn. Some strong Q or a set are certainly possibilities, here, but so are two hearts or even A4.

The turn bet was relatively small, so it might have been a probe to try and steal an orphaned pot -- that's always a possibility. Villain figures that a 4 didn't hit the preflop raiser and that you already said you didn't have anything worth pursuing, so he's going for it. Because of all that, calling the turn seems appropriate to me, but only because you're closing the action.

On the river I'd fold. Unknowns generally don't bluff with a pot-sized bet; rather, they bluff with a half-pot bet. If he'd dropped $5 on the river, I'd call it. As it stands, I'm moving on. Even if villain is panic-betting his T he's got me beaten, and I think villain's range is loaded towards two-pair and trips which beat me soundly. I've got no folding equity unless I'm ahead, and I think I'm behind more than 2/3rds of the time, so I let this one go.

Note that if you change that T to a 5 and I call this river bet.