Just to recap the action, you've got a "pretty loose" SB who has check-called you to the river, then all of a sudden check-raises you on the river.

I think that you should 3-bet here, but if the SB 4-bets, you should just call. If SB 4-bets, you should call rather than fold b/c the pot has become so large that folding 10+BB pot to 1 bet is unsound limit poker strategy. Any likely hand that he has that would beat you would probably have been check-raised on the turn. If he had a set, A-K for top 2 pair, or an Ace-high straight, most players would have check-raised the turn. It's very unlikely that he's got 7-9 for a runner-runner straight, and it is equally unlikely that he would check-call you down to the river with pocket 8s.

Having said that, his most likely holdings are 2 pair, and probably not A-K. I would put SB on either A-8 or K-8, both of which you can beat. Because you are likely to have the best hand given the fact that he didn't check-raise the turn (the classic street for check-raises), I would 3-bet, thinking that your two pair are good.