As others have said, hard to know the full context of the hand. Stack sizes are very important in this spot with the relatively large sizing for the villain on the flop and turn bets. Tendencies of the players are also in play. But in a vacuum, the line that you have described isn't as bad as others might think. I think most importantly is noting what 2 diamonds rolled off on the flop. Jd9d2c based off the line could make up a very different range of villain then Jc9d2d
Let's start with preflop. Without stack sizes in play I am going to assume that this is 100BB and that you are playing 2-5, since a 15 bb open is some pretty wild texas stuff at a classic 1-2 or 1-3 game. Let's also assume you are 9 handed (wouldn't change that much with a CO and Button range, but still). And lastly we will assume that villain is a competent reg, no nitty OMC or loose aggressive nonsense. 9d8d is a fine open from the CO for 3bb. Villain's calling range in this format if they do not raise us preflop we rule out TT+ and a lot of high suited broadways. Mostly they have ragged aces, low suited aces (assuming they call those at a high frequency and don't 3-bet them IP), marginal broadways, middling suited connectors, and 99-. We opened for 3bb, 7.5bb in the pot, with 92.5 behind
I will preface this with the note that I have been watching and employing a lot of Hungry Horse's poker strategy and the check OOP on the flop is not out of the question. It let's us see what range of hands villain has. Let's assume the flop is Jd9d2c, as that looks better for your hand vs a button calling range (Rules out a higher flush draw with top pair i.e. QdJd, JdTd, etc.). With this range our middling suited connector has a lot of equity with a flush draw and gutshot and doesn't want to get blown off the hand if we face a check raise with the top of villains range or a bluff. So a check does make a lot of sense here. You could go for a bet and take the betting lead, but what if you don't hit your straight on the turn? What if you don't hit your flush? Do you stop betting? That seems like playing your hand more face up then checking. It does limit your overpairs, but you can still have the Ace high flush draw (AdKd, AdQd,) or could be slow playing a set of Jack or sometimes Nines. These all can be repped with a check-raise on flop or sizable bet on the turn if it gets checked to you. With villain betting 2/3 pot (5bb), they are telling us they either have a flush draw (which is probably better then yours) but more likely a Jack, TxTx, a set, or sometimes two-pair with Jx9x. They bet 5bb We end here with 17.5bb in the pot and 87.5bb behind
So we get to the turn which is all intents and purposes a blank. We still have our draws and we are reducing villain's range to mainly top pair or better. I assume that some semi-bluff flush draws such as the naked AdXx and otherwise will shut it down and take their equity. Leading here does not make sense as I do not see you folding out any of those better hands and the bluffs villain might have might have you beat non-the-less. Check here as played is the way to go. They bet 12bb, 42.5 is the pot with 75.5bb behind.
Now we make our flush draw, and no straights are possible. At this decision point do we check, or raise. Well let's see what value we beat. JxXx of course, Jx9x, and a set of nines some TxTx that play this way. For flush draws that we beat... None? Flush draws that got there that beat us? AdXd that are not AdQd or AdKd. 5 combos. And other broadways suited broadways that got there KdQd and KdXd at some frequency, KdTd, QdTd (Which is their best semi bluff candidate). 4ish more combos. We can give them 5ish of these better flushes because they might shut these down on the turn. Their bluffs here like Qx10x are few a far between and will probably check back anyways (player dependent). Looks like we have value here. Most of the things we beat are not going to like a big bet such as their 1 pair hands. I would say a 1/3-1/2 pot sized gets a call from top pair and better. Put in 20ishbb for a pot of 62.5 with 55.5bb behind. Fold to a jam because I think pocket 9s would probably just call at a high frequency and there are only 3 combos of that anyways (again player dependent because I have seen folks make this move with a set of Twos, Sixes, Fours).
That's my take anyways.