Really nice post Erpel

Aha! Thought original poster had Tight image and that villain was LAG.
That changes everything.

Playing 44 preflop is EV- with a LAGGY image IMO. You can not assume fold equity with that image, and therefore 44 becomes a set or fold hand (which sucks).

As played I would check-raise(Pawnalot style) turn, because I do not think he has AK, AQ often enough and he will fold all pairs. We still have some equity if he calls.