Your 3-bet size isn't helping your cause at all here. You're OOP and mega deep, so I'd make this at leassssst $20, if not more.

As played, I don't think he's really gonna play QQ/KK this way given how deep you are, despite your read that he raises hands he plays.

As nitty as it is, I don't even mind a fold that much here vs this opponent. If this was madman, thats a different story. You can't really go stacking off 300bb deep postflop with overpairs, after you gave him a good price pre to sethunt.

If I'm continuing, I'm always flatting. There's no reason at all to raise here, against this opponent.