A Very Weird Fact About Venus

I was playing around with numbers trying to understand things, and wanted to calculate the mass of Venus's atmosphere. I knew its surface pressure p_s was 92 times Earth's, and the mass of the atmosphere can be obtained from

M_atmg = p_sA 

where g is the surface gravity and A is the planet's area. (This assumes g is constant throughout the atmosphere, which is a good approximation for these purposes.) The planetary data is here and here.

To my surprise I found that the mass of Venus's atmosphere is 92 times Earth's, the same ratio as the surface pressures. Why would that be?

Since g=GM/R² and A=4πR², this means the ratio

M/R⁴ 

must be nearly the same for both Venus and Earth (M=planet mass, R=planet radius). And they are, to about 0.1%.

Why? There's no reason I can see; they just are.

Am I missing something obvious? It's late and I've been working all day....

(By the way, this isn't true for Mercury or Mars.)