My read on this situation is that you are currently ahead of the villian. THe hand that he most likely has is Ad Jx.
Other possible hands include QQ, KK, AA all of which might contain a diamond. Given this information I think the best play is to give him incorrect odds if he wants to continue to draw to his flush or potential 2 outer with a higher set.

I think the correct play here is to raise to $1800-2000.

If he pushes I think you still must call. He could very possible have JJ or 99 which you are dead. However, I still think he will push with AA, KK ,QQ, AdJx and then it is correct to call.

In response to another question, yes I think it is weak tight to fold here. There is no justification in my mind to fold. I cannot see the villian betting into that flop with a flush because there is already a person all in.