Using your scenario, I would probably bet smallish hoping for a reraise. If I bet big, I'm thinking he's going to fold to a show of strength. A weak river value bet - third pot? - can create doubt in opponent's minds as to whether or not you've made a strong hand, and perhaps induce a re-raise.
If the opponent simply calls the small bet, it would suggest to me that a larger bet might have gone uncalled. If he re-raises, or pushes all in, I'll have gained good info for future pots played with him. I think there's value in that knowledge just as there's cash value in the game.