The villain is a 22/13/1.0 guy who seems generally passive and who folds SB to steals 73% of the time.

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG ($32.80)
MP ($25.35)
CO ($26.45)
Hero (Button) ($25.25)
SB ($33.30)
BB ($93.95)

Preflop: Hero is Button with 10, J
3 folds, Hero bets $0.75, SB calls $0.65, 1 fold

Flop: ($1.75) J, 9, Q (2 players)
SB checks, Hero bets $1.50, SB calls $1.50

Turn: ($4.75) K (2 players)
SB checks, Hero bets $3, SB calls $3

River: ($10.75) A (2 players)
SB bets $10.25, Hero ?

Preflop: Standard steal

Flop: pair+OESD with FD on board. While 27% (his calling %) includes a ton of broadways (pairs/two pair/sets) it also includes lots of suited aces and connectors. I think a semi-bluff here is the only possible move. Building pot in case we hit our straight, get value from unpaired hands (like Axs) that we beat with our pair and folding out some hands that may have some equity against us and picking up the dead money.

Turn: We complete our straight and pick up a flush draw (1 out to the straight flush). Two pair hands and sets we now want to get value from and AcXc and other flush draws we want to price out. Our straight is only a K-high straight, so a holding of AT still beats us.

River: Funny card. In a sense both a good and a horrible one. Having it be the Ac that completes the flush eliminates half or more of the possible flush combinations. We now have the A-high straight so anyone holding AT is now splitting with us.

BEFORE betting I put the opponents range at this:
99-QQ, KQ-K9, QJ-Q9, JT, T9

You could well argue that some two pair hands and sets (99, JJ, QQ, KK, KQ, KJ, K9, QJ, Q9) should be discounted as they may have folded the turn facing a 4-to-a-straight.

When a passive opponent chooses to make a bet here that is exactly pot sized ($0.50 off due to rake) it's not just any random hand. I have to at least emphasize KcTc (Royal Flush), Kc9c and Tc9c.

If he were to pick hands to bluff with TcXx hands seem quite obvious as he would have a blocker to the club flush.

The thing is. The exactly pot sized bet from a passive opponent is so uncharacteristic of him that it must denote a very narrow range. With such a narrow range a single combination that we still beat is almost enough to make a call mandatory - and a couple of combos that we split with likewise.

In retrospect I think I may have been wrong to bet my pair+OESD on the flop. If I improve, I might be improving to a second best hand so I might actually have a reverse implied odds hand here. It may have been better to check behind and pick up the aggression on a safe turn (or one that completes the straight)

So what do you think? What's his river betting range?