I don't love the overbet here. I'd rather overbet with a strong hand on the river when an obvious draw bricks or something.

Assuming you bet turn and check back bricked rivers, you need to make about $1.40 on average everytime you hit the river (assuming 20% turn equity). If you are over-betting $2 here, you need to get called 70% of the time you make this bet. I don't think you get called that often to this size of bet.