Consider a "weighing machine" as simply a force gauge that measures force perpendicular to a surface that is applied by the surface, or the normal force. In this case, it is measuring the force applied by the ground to the inclined plane. The two key principles we need are Newton's 3rd and Newton's 2nd laws. Let's examine the first scenario, all objects are stationary. What are the forces acting on each element of the system? Well for the block there is gravity pointing downward, which is opposed perpendicularly to the surface of the plane by the normal force of the plane on the block, and opposed parallel to the incline by (let's say) friction. Now what are the forces acting on the incline: naturally the equal and opposites to the normal and friction forces applied by the plane on the block. Additionally, there is gravity acting (downwards) and the normal force of he ground on the incline (this is the particular force we are measuring). (Note If we constrain the incline to not move horizontally, there must also be some "friction" force applied to the incline, but as it is perpendicular to the force we are measuring, it's doesn't really need to be considered). When everything is at rest these forces sum to 0 for each object.
Now let's examine the case where the block is sliding (let's say without friction). Thus the opposite friction force acting on the incline is absent. As we still assume the incline is stationary (or most importantly, stationary vertically) our normal force applied by the ground on the incline must change to meet the requirement that the net force on the incline is 0.
To explicitly carry our the calculation I would recommend drawing out a free body diagram and summing the forces accordingly. Hope this helps.