JJ is hard to play!

[AnthonyH]

"I am OOP"

Bump it up pre-flop to make post-flop decisions easier. There's a good chance you down pre-flop and if not at least you drastically narrow his hand range down. Calling and running into a flop like you did with JJ OOP is even worse.

"facing a larger-than-usual raise from an unknown-ish player that I have just bet off a couple of hands."

The fact that you have blown him off the last few hands may mean he's getting frustrated. Regardless, JJ is ahead of even the nittiest players opening range. Raise for value.

"I am holding a medium strength hand with a player to act behind me"
Raise for isolation. Flat calling allows lower pairs and suited connectors in for cheap. Not what you want with JJ.

"It is a hand I want to continue with, but a hand I cannot call a 3 bet with"

Against a loose and aggressive player whom I've bet off a couple hands I wouldn't mind playing JJ for stacks.