What you are doing with this method is making the plane a plumb bob, as well as the independent weight. It is quite a simple concept that the CG of both objects will hang straight down - and their CG's will lie along the same line when hung from a common pivot.

AS far as acually locating the CG, it doesn't matter if the plane hangs level. The CG of the plane will hang under the plumb-bob no matter what the attitude. However, since most people are trying to find the CG longitudinally, it is easiest to find when the plane hangs level.