Does the momentum of the wheel cancel the weight of the pebble?

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I've just seen how applying a force on one axis of a gyroscope results in a movement on a completely different axis.
Is the weight of the entire apparatus affected by the weight of the tiny rock? What I'm trying to ask is, if we put a scale under the pic related, would we get a different reading?
If not, is it possible to somehow redirect the reaction from Newton's third law into a different axis as to not affect said scale? I know we have to conserve energy, I just want to take the energy from the rotation of the wheel to cancel the force generated by gravity.