I'll play...

Raising 6x from the BB I would assume 99+ or some mixed broadway. If really loose, maybe lower pp or suited connectors trying to buy the pot straight out.

He then checks the flop but only calls a 1/2PSB. So now I'm thinking a made overpair is unlikely 'cause he would have either led out or CR to try and push out your possible OESD. This doesn't happen. But he still likes his hand enough to not be able to lay it down. To me that's probably AK, AQ or KQ. Of these, I can only see AK or AQ making the PF raise OOP. The other option is 56 or A2, altho' I don't really like either of those for the PFR either.

He checks through the turn, so TT is definitely out of the picture. And checks through the 7 , meaning 56 is done... and I didn't really like A2 anyhoo.

So that puts me on AK or AQ.