I am possibly saying something very stupid with this post, but lets hope I'm right...

Villains raise range is 166 combos, 19 of which we block since we have A9s.

Villain will call with 42 of these 147. 42/147 = ~28%.
The pot when it comes to us is 5.5BB (SB+BB, villain raised 4x). We are going to 3bet him to 12BB so we're adding another 11 to the pot.
From villains point of view, this is calling 8BB for a total pot of 24.5BB. 8/24.5 = 0.3265. Villain needs to be in his 3bet calling range 32.7% of the time to make this unprofitable for us.

Since his 3bet calling range is 28%, and 28<32, 3betting with A9s is profitable for us.