It seems there might be some confusion in your question. Gravity and gravitational waves are not forms of geodesic deviation; rather, geodesic deviation is a concept used to understand the effects of gravity and gravitational waves.
Gravity is a fundamental force that attracts objects with mass towards each other. It is described by Einstein's theory of general relativity, which explains gravity as the curvature of spacetime caused by mass and energy. In this theory, the motion of objects, including light, is affected by the curvature of spacetime, resulting in the force of gravity.
Gravitational waves, on the other hand, are ripples in the fabric of spacetime itself that propagate outward from massive objects undergoing acceleration. They are caused by the acceleration or movement of massive objects, such as the collision of black holes or the merging of neutron stars. Gravitational waves carry energy away from the source, similar to how electromagnetic waves carry energy away from a vibrating electric charge.
While both gravity and gravitational waves are related to the curvature of spacetime, they are distinguishable from each other. Gravity is the force that attracts objects with mass, while gravitational waves are the disturbances in spacetime itself that propagate through space.
As for your question about an ideal weight scale detecting gravitational waves, it is highly unlikely. Gravitational waves are incredibly weak and diminish in strength as they propagate through space. The effect of a gravitational wave passing through an object, such as a weight scale, would be extremely small and difficult to detect. Currently, gravitational wave detectors, such as the LIGO (Laser Interferometer Gravitational-Wave Observatory), use extremely sensitive instruments designed specifically to measure the minuscule displacements caused by gravitational waves.
In summary, gravity and gravitational waves are distinct phenomena, with gravity being the force of attraction between objects with mass, and gravitational waves being ripples in the fabric of spacetime. While both are related to the curvature of spacetime, they have different characteristics and are distinguishable from each other. Detecting gravitational waves requires specialized instruments due to their extremely weak nature.