Villain is a weaker player running 31/14 and no folding very often to 3bets.

On flop I think I think both betting and checking is reasonable as we have Ad so can call on most turns and pick up bluffs but at the same time betting to set up future barrels to fold out mid pairs seems a good option as well.

I think turn is a mistake but I often end up getting caught between two strategies in these situations. Is it reasonable to just try and get to showdown against his worse ahigh hands and other worse hands or should I try and fold out weaker players that often call once but then fold to more than one barrel.
This is also more of a general question really in terms of what factors to look for when deciding whether to simply try and showdown a hand like this or deciding whether to turn it into a semi bluff almost with the overcards and bdfd,