Will he fold a better pocket pair than yours?

Most players will just call down with JJ TT etc when they are heads up and a Q falls. I cant see him check raising JJ against you, after your preflop 3 bet.

You are bankning alot on if he would fold JJ-99 (b/c you can beat overcards).

I say fold preflop and dont put yourself in these situations against a TAG who may checkraise AK