I think I was playing this hand down with pot odds and couldn't put the player on any reasonable hand. Turns out he was bluffing all the way until the river.
Hand converted with online PokerStrategy.com hand converter:
$0.05/$0.1 Fixed-Limit Hold'em (9 handed)
Preflop: Hero is BU with A:c, J:d.
2 folds, MP1 raises, 3 folds, Hero calls, SB folds, BB calls.
Flop: (6.4 SB) 3:s, 4:h, 7:h (3 players)
BB checks, MP1 bets, Hero calls, BB folds.
Turn: (4.2 BB) 9:c (2 players)
MP1 bets, Hero calls.
River: (6.2 BB) A:h (2 players)
MP1 bets, Hero raises, MP1 calls.
Final Pot: 10.2 BB.
Results follow:
MP1 shows a pair of aces(Ad Kd).
Hero shows a pair of aces(Ac Jd).
MP1 wins with a pair of aces(Ad Kd).