Betting the river there is pretty terrible. Betting the turn ain't so great either.
Limping the SB is bad, your raise on the flop is small, pretty much I don't like any action in the hand. Sorry
So um, lets start at the beginning:
1) You're spewing reverse implied odds
with a hand that's really only going to make top pair. If the table is tight, raise this, but there's no excuse for playing a hand that is unlikely to hit a flop well out of position with no initiative. Do you really want to limp A9 and spew off a bunch of money to set mining tight players when you flop your ace (since that's really the only thing tight players limp with, small pairs)?
2) Just lead the flop. Check/raising makes a large pot where you want one, and its possible they could check back weak draws & middle pairs that hit on the turn. Lead the flop for like 50c.
3) Leading the turn again isn't bad. If its a tight table as you say, then check/calling is by far the best line. But since its 10$ NL and its probably not a tight table, leading for that size a bet is fine.
4) Check/call the river every time! A8 is the best hand that you beat, and he's probably not calling another bet with that. Draws make up a huge part of his range. By checking, you allow him to bluff those busted draws. You cannot get 3 streets of value from this hand (yet another reason not to limp it in the first place). Betting this river is a big leak IMO.