grunch:

Bet flop, bet-fold turn. Pot is small and any other pair will beat you on the turn. I would probably never have made it to that river, but since you did, you might consider check-calling. Since the pot is small, even passives might take a stab, thinking no one will fight for it. Then you don't get raised if they actually have the straight.

No one has shown any interest whatsoever yet, so you don't have much reason to think they even have a pair, making a value bet thin to nil.