I'd flat and let him barrel away oop. Depends how deep he is really and how deep you are. I don't think he is just putting a flush draw in that easily if your raise unless he has pair+draw but your beat by two possible set combos and only beating A3 or the occasional AK AQ he does this with. But again I don't think he overplays those as a solid player if your calling down every street. A raise all in might push him off all the hands your beating other then sets and A3.

Very clear call. BB caller has a lot of flushes in his range, so we're definitely not super happy about the situation, but we do have good enough hand to call, sometimes win versus bluffs and sometimes improve to a full house. Certainly not 3betting!

Unless you think villain is going to do something stupid with the K fd then raising has no value, you fold out his draws and lose the value from his bluffs.