Playing back at high card raiser at final table

[betgo]

Stud high tournament I am in 5th place of 8 with T5200. Villain has me covered. 300/600/100. Upcards are 288K6J53. King up completes, I reraise with split jacks. He calls. 4th street he has K4, I have J5. He checks, I bet, he calls. 5th street, he makes an open pair of 4s and bets, but I am pot committed. 6th street I make an open pair of 9s for two pair. All the money goes in.

Villain had concealed aces and wins with aces up.

Was I right in playing back? I figured villain probably didn't have kings and if he did I had some chance. He might have a lower pair, a draw, high cards or nothing. I probably played it OK, but am upset about busting out.

I think villain played it too slow. I didn't have that many chips, so I don't see the why he didn't reraise on 3rd street and bet or checkraise 4th street. What's the point in trapping. I obviously had jacks or something else strong and he shouldn't mind if he could somehow get me to fold.