Simple Theory Question -- facing a 3bet NLCASH

[APXG]

I've been having a lot of trouble thinking about this recently.

Lets assume 75bb stacks i.e. 1500 on 10/20 level. Hero raises to 2.5x or 3x and gets 3bet to 9x i.e. Hero raise to 60, Villain raise to 180.

Villain is solid, and fairly aggressive, but not overly so. So expect him to be 3betting whatever you yourself would be vs. an unknown who raises 70% of hands from button.

How do we play a hand like JJ or TT? If you say 4bet shove, I know, thats easy, but lets say you can't shove. Do you 4bet to a smaller amount, ever? Why / Whats the plan if you do?

Regardless of your answer for above, lets say you call. 18bb in the pot, ~65bb effective. Flop is Axx or Kxx or Qxx. Villain bets 13bb. Call? Raise? Plan for turn? Say it puts out a big draw, and he checks? Can we bet? Can we call a check-raise allin?

This is one of the few spots in HU SNG where I just get really puzzled. It seems like the villain is ALWAYS outplaying me, regardless of whether I win or lose.