No-Limit Hold'em, $2.00 BB (5 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

MP ($200)
Button ($200)
Hero (SB) ($482.30)
BB ($210)
UTG ($91)

Preflop: Hero is SB with A, 9
3 folds, Hero bets $7, BB raises $24, Hero calls $18

Flop: ($52) K, K, K (2 players)
Hero checks, BB checks

Turn: ($52) 4 (2 players)
Hero checks, BB bets $34, Hero calls $34

River: ($120) 3 (2 players)
Hero checks, BB bets $80

Total pot: $120

So villain is 3betting 12% vs steal in bb, we didn't have any history of me 4betting him just yet, so I wasn't sure A9s was strong enough to 4bet call it off here. Maybe it was, not too sure.

As far as postflop goes, I can't think of a hand he checks behind the flop yet value bets both turn and river. I certainly can have a hand like 88/99 that would call both turn and river. At first I thought villain may have had something like AQ after checking behind the flop, I would have expected him to bet AA/QQ/JJ though really unsure. His line doesn't make a whole ton of sense to me and I'm having trouble figuring it out. Thoughts?