Not sure about the villain looking solid, his line is bizarre?!
Dont think he shows up with a min raise pure bluff here all that often tho??
Some kind of 3 (A3,34,35) is possible if he puts you on an OP so is not worried about the FD's ?? Would think he raised his PP's pre, but I guess 66 is possible also... These are the only hands I can think he plays like this that beat you... the rest must be made up of club draws (spade draw got to be unlikely given flop call, although AsTs may do this??)
Might be way off with this, but thought I'd give it a whirl... left big Aces out assuming he raises pre with these
Text results appended to pokerstove.txt
2,112 games 0.005 secs 422,400 games/sec
Board:

Dead:
equity win tie pots won pots tied
Hand 0: 41.098% 41.10% 00.00% 868 0.00 { JdJh }
Hand 1: 58.902% 58.90% 00.00% 1244 0.00 { 66, AsTs, Ac9c, Ac8c, Ac7c, Ac6c, Ac5c, Ac4c, A3s, Ac2c, KcQc, KcJc, Kc9c, Kc8c, QcJc, Qc9c, Jc9c, 9c8c, 9c7c, 8c7c, 8c6c, 8c5c, 7c6c, 7c5c, 6c5c, 6c4c, 5c4c, A3o, 53o, 43o }
---
2,112 games 0.005 secs 422,400 games/sec
Only thing he folds if you shove, is complete bluffs which I dont think he has very often ?? You could also argue he shoves/calls the turn with a draw himself rather than min rasie, so range above may not be all that accurate, you could be alot worse off than 40%
Sat here its a fold for me, probs shove if I'm at the table cos I'm a spewtard and have an overpair
nb.. Interested to know if you good people think this range is realistic or whether Im way off... ta