Villain is 38/29 over 24 hands.

PokerStars - $0.50 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

Hero (SB): $57.07
BB: $50.00
UTG: $50.00
CO: $51.51
BTN: $50.00

Hero posts SB $0.25, BB posts BB $0.50

Pre Flop: (pot: $0.75) Hero has K A

UTG raises to $1.50, fold, fold, Hero raises to $5.25, fold, UTG calls $3.75

Flop: ($11.00, 2 players) K T 9
Hero bets $6.75, UTG calls $6.75

Turn: ($24.50, 2 players) 2
Hero ???

Alright, so I'm not really sure what to do on this turn. If I bet, I think am committed to calling off a jam and I don't really want to give up control of the pot by checking either and possibly giving a free card.

If we assume villain gets to the turn with;

www.pokerstrategy.com
Board: KhTs9s2s
Equity Win Tie
MP3 40.71% 38.30% 2.41% { JJ-99, AsQs, KdQd, KhQh, KcQc, AsJs, KdJd, KhJh, KcJc, QsJs, KdTd, KhTh, KcTc, AsKd, AsKh, AsKc, AsQd, AsQh, AsQc, AsJd, AsJh, AsJc, AsTd, AsTh, AsTc, KdQs, KsQd, KsQh, KsQc, KcQs }
SB 59.29% 56.89% 2.41% { AdKs }

That's 42 combos. He prob jams with;

www.pokerstrategy.com
Board: KhTs9s2s
Equity Win Tie
MP3 55.00% 50.91% 4.09% { TT-99, AsQs, AsJs, QsJs, AsKd, AsKh, AsKc, AsQd, AsQh, AsQc, AsJd, AsJh, AsJc, AsTd, AsTh, AsTc }
SB 45.00% 40.91% 4.09% { AdKs }

Which is 21 combos. If we assume villain doesn't just flat again on turn, which is unlikely given remaining stack sizes and board texture, he is folding the other 21 combos.

Thoughts on ranges and next course of action?