Thank you good sir. You make a compelling argument. I am inclined to agree, the current system with only gems will not work. However I think I can fix it with a few small changes.
By attatching both sets of fabrials to large blocks, so that the total weight of each System is 100 Kg, and assuming the weight of System 3 is less than that of System 2 will result in the following
System 1 will drop 1 meter and because it is exerting ~166 Kg of upwards force on System 2, System 2 will be brought up 5 meters
Upon the disconjoining of gems A and a System 2 will drop 4 meters, and System 3 will move 4 meters
Upon the conjoining of gems B and b both Systems 1 and 2 will have the same effective weight, however since System 2 has momentum behind it it will fall 1 meter raising System 1 by 1 meter.
I'm pretty sure that will work. And if not we can adjust gems B and b to be different sizes
However we can do more
First we mount fabrails on the top and bottom of System's 1 and 2, capable of both attracting and reppelling air. When a System falls the fabrial on the bottom will repel air, enableing both systems to fall in a vacuum. And the Fabrial on the top will attract air, making the system experience greater pressure than it otherwise would. When raising the effect will be reversed, creating a vaccum above the system, and increasing pressure bellow it.
Does that work or am I completly stupid?