PokerStars No-Limit Hold'em Tourney, Big Blind is t30 (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

SB (t1020)
BB (t1615)
UTG (t735)
Hero (t1235)
MP1 (t3110)
MP2 (t320)
CO (t2610)
Button (t2855)

Preflop: Hero is UTG+1 with K, K.
1 fold, Hero raises to t150, MP1 calls t150, 4 folds, BB calls t120.

Flop: (t465) A, J, 2 (3 players)
BB checks, Hero bets t250, MP1 calls t250, BB calls t250.

Turn: (t1215) 8 (3 players)
BB checks, Hero checks, MP1 bets t150, BB calls t150, Hero folds.

River: (t1515) T (2 players)
BB checks, MP1 checks.

Final Pot: t1515

Results in white below:
BB has Th As (two pair, aces and tens).
MP1 has JavaScript 9h (one pair, jacks).
Outcome: BB wins t1515.

I'd play it the same. He'd take the free river with a club draw and he isn't betting a Jack.