I have no problem with calling pre. You have ~40% equity against the range you assign to him after all.

I feel he cbets all his range on that flop. Yes this differs from his cbet stat but if he 3bets that tight then we don't know how he plays the flops which he 3bet pre and I expect him to be aggressive with all his range... So I can't exclude QQ from his range with only 1 cbet. Also, I beleive that cbetting QQ on these kind of spots is one of the most common mistakes we micro stakes players make...

Now his range contains 3 AA, 1 KK, 6 AK, 6 QQ. And against that range your equity must be something like 55%. Raising here accomplishes nothing obviously, folding is giving up on a lot of equity since we only need 25% equity while we have 55%. I would call this. On the other hand, if he barrels the turn I'm definitely removing QQ from his range and fold (except a K on the turn of course).