Weight of Fast Rotating Gyro - Does Angular Velocity Increase Weight?

[leave]

there is a gyro...

put it on an electronic scales which has a smooth surface...it shows the weight is M.

then, let it rotate... keep increasing the angular velocity...

will the weight display increase? or else?

 

[mfb]

Does its rest energy increase? Where "rest" refers to the center of mass of the object, not to its parts.
Proper scales measure the rest energy of objects.