Preflop
You don't mention any facts about the other players nor how many are at the table. If it's a full table JTs is a bit marginal to call with out of position.
Flop
You hit the flop big-time. I like that you bet out (I would have check-raised though), his raise might indicate that he has at least AQ or AA/KK. Here you should PUSH! I think calling is wrong, you have a huge draw and want to get the cash in while you're a favorite, add in fold equity if he's on AK, JJ (or capable of folding AQ or an overpair). I push here every time.
If I had flopped a set of 9's here I would bet out like you do, hoping for a raise so I can push, in this case I would chec-raise all-in instead though.
Turn
Well his all-in probably means an overpair, or a horribly overplayed AK. I think you just about have the odds to call if your 15 outs are live (which they should be, but you could be missing 2 Kings if he has KK, so you're hoping for AA or AQ).
Personally I think you played it wrong and a bit loose/weak. What were you looking for when you called a raise with suited connectors? A flop that could break someone with an overpair. You got it but waivered at the critical moment (he who hesitates dies!).
