I hate playing these medium overpairs into aggression. His $4 into the $8 flop could be AK AQ etc. So I like your re-raise, that would be my standard line too. However I am looking to take down the pot there generally if they come back your pair is counterfitted. To me his push looks like QQ+ scared of the draw. He probably has AA or KK. I would fold this here, after all why were you raising, I assume not to take your stack to the felt but rather for information/build pot? He has provided this and it's time to use it. The two-dimes stats confirm this especially with your reads.

Also I like his play caus I can note 'wont escape AA post' in his notes and look for the set any other time we play! I don't play $100 tho so maby my view is off.