[orlov]

Okay, after learning to read my second attempt at this :P:

Assuming his 3bet calling range is somewhere along the lines of TT-QQ,AK you are ahead of his range on the flop:

equity win tie pots won pots tied
Hand 0: 69.345% 67.51% 01.84% 17377 472.50 { QdQh }
Hand 1: 30.655% 28.82% 01.84% 7418 472.50 { QQ-TT, AKs, AKo }

Your check to him showed weakness, but he still has CO to act behind him, so I dont think this is AK getting fancy.

Thus we can narrow it down to QQ-TT imo. If you assume he was scared of 4betting KK pre, your equity goes down tough.

equity win tie pots won pots tied
Hand 0: 63.197% 58.42% 04.77% 5784 472.50 { QdQh }
Hand 1: 36.803% 32.03% 04.77% 3171 472.50 { QQ-TT }

I would just raise it to 2/3 pots and see where it goes from there.