4 bet or just calling the 3 bet with AQs?

I wanted to know how I played this hand and how you would play it.

if he had gone all in pre-flop it would have been a difficult spot too.

so I thought maybe just calling would be a better play to control the pot and to keep my opponents range wider.

so if I had called pre flop I should have bet on the flop right? Or check call? Check raise? What about the turn and river?