77 with overcards vs double barrel

Pre you cold 3bet IP. It's +EV for sure. Calling fine as well.
The rest seems decent. He could overbet that turn because you are capped, but he's not aware of that probably.
It's fine to call OTT with position, although I prefer to fold. You have enough 9x I suppose to defend (A9s-J9s) that also block AA-QQ hands that make the top of his range.
As played, just fold river. Price is not terrible with a full though, but no one is aware of how wide they're supposed to barrel this.

You have enough 9x I suppose to defend (A9s-J9s) that also block AA-QQ hands that make the top of his range.

I don't understand this argument, can you elaborate?

EDIT: Oh you mean that I'll be holding 9x here often which balances this fold with a PP lower than 9x, and that'd be a good call partly because those 9x hands block AA-QQ?

If you have a 9 high full house, which is better than the 77, your 9x will be A9, K9, Q9 and J9 mostly, that benefit more from blocking his strongest full houses (AA-JJ).
Yeh, defend here with 9x or better is enough for sure against their tendencies.