My standard open would be a little bigger around bubble (depending on BB stack and 3b%). Put pressure on short stacks. His 99 flat on button is odd (assuming he is folding if one of the blinds shoves, but allows the blinds to see flops profitably against 99. I think a player flatting here is still flatting to 3x, so nothing changes.
1. I dont think you can bet small and fold as you will have a STP ratio under 1.
2. checking allows him to check behind with Ax, and one pair hands,
3. check / folding seems to weak.
4. shoving is only targeting TT and JJ and A9s, but will deny equity to overs. I dont see AK in his range, unless stone cold bubble and his is super tight, so denying equity to the few Ax hands he has here doesn't really matter.
I think if he was biggest stack left to act PF, I just profitably shove a 14bb range rather than having an open range from CO and Button to apply maximum pressure. If one of the blinds is a bigger stack i go to a 2.2 - 2.8x with big hands some i intend to call off and some I intend to fold to 3b from bigger stacks.
No matter how you played this one, someone that flats button with 99 here will only be set mining with incorrect odds and he got lucky that you had an overpair the time he hit his set.