JJ Hand. Should I raise the turn?

I think your beat on the turn, and only an A can save you, when you will almost certainly be splitting the pot with 4-to-a-straight, which halves your odds at least. A J won't save you either, for the same reason. *

Fold the turn.

* Not the same reason, the reason is in fact that a set will be beaten by a str8, which will certainly be made by a J on the board

[Songwind]

For 14.5 to 1? I'm not confident that I'm beaten often enough to fold with the pot this big.

the odds aren't that good because you will probably be splitting the pot.