I think in this situation If I flat is to be able to lose a small pot since as you have demonstrated His shove calling range is flipping vs 99.
So I guess I flat Turn which is a $6.00 pot with effective stacks of $12.
Here would be my spot to value bet if it comes anything but Q+, x

since will be OOP and from his aggression he seems like he's the type that will put me on a shove or fold decision on turn if I check to him.