The system move down but a mechanism limit speed at 100 m/s (for don't have acceleration: easier to calculate).
Then, the most important part is that mechanism. Every unbalanced external force would come from that mechanism. (System staying on the table would be simpler to talk about, and the same by physics.)
While the spring contracts, it moves the column down
with respect to the water. Since the column cannot move down faster than its constant speed, then the column would be supported by the mechanism, and would receive
an additional external force from it. And that force would move the center of mass.
But if speed is at 10 m/s the work giving is not the same (for me).
That's no problem. The work is always different for different speeds and reference frames. The only thing that keeps the same is balance. If there is an energy balance for one reference frame, then it would be for another. If there is no balance, then no. If some energy have become heat, then the heat would be the same in another reference frame. (Heat may change if you change the actual speed of motion, not the speed of reference frame.)
It's for that I think the weight is always the same. But if the weight is the same (no additionnal force), when I move down vacuum and move up water, this change the center of gravity I think.
You cannot move the center of mass without changing the weight (or without applying any other external force).
There is a theorem about the motion of the center of mass. The center of mass always move the same way as if there would be a point mass at its position, and all external forces would be applied directly to that point mass.
I recommend you to refer to the textbooks on Theoretical Mecanics (Analytical Mechanics, Classical Mechanics). For one example, there is a (popular in Russia)
Landau, L.D.; Lifshitz, E.M. Mechanics (Course of Theoretical Physics, Vol. 1).
Any other good textbook will do. (I am sorry for naming none, I am not familiar with textbooks in English or French.)