This is going to depend on a lot of things and not just your small pair. That same small pair will be played differently in every possible scenario. How did you arrive at this river, how many opponents are you up against, what is your stack depth, what are your opponent’s stack depth, what is the player profile that I am playing, are they a Station, Maniac, etc etc etc.
You want to really think about what the purpose of your bet is before you even make it on the river. You no longer need protection, because you are at the river now. So it’s either a
bluff or it’s for value. If it’s for value, then you are targeting a worse hand to call you with. With a small pair that means you are targeting an ace high hand. How much can you bet and get an ace high to call you here?
If you don’t think an ace high will call then you are
bluffing with this bet. So now we need a better hand to fold. What bet size will accomplish this?
If we go too small a better hand will call and we don’t want that. If we go big it might fold out a better hand but the really good
hands that made it to the river with you will call or raise you.
if you don’t think you will accomplish anything with your bet then don’t bet. Just check. You have showdown value and can win if the villain checks into you here. Same as if you had an Ace high hand. Betting here can be a costly mistake.
Anyways, things to think about with the River Bet: What worse hand can call, what better hand can fold, how do I size my bet to accomplish this.”