Pulley system with one mass and apparently independent forces?

[Maurice7510]

So at my gym, there's a cable machine that works like this: You pull on one cable and you lift x mass using y force. You pull the other and find the same thing. If, however, you pull on both, you're still only lifting x mass (you can see the weights) yet somehow each cable is still requiring y force. I actually held ~80lbs in both arms, and then released one. Intuitively, I should then be resisting 160lbs with one arm, which aside from being well beyond my ability, should have at least been noticeable. Yet I found no noticeable difference at all.
I was just wondering how a system could be set up to allow for this kind of thing.

 

[A.T.]

You pull on one cable and you lift x mass using y force. You pull the other and find the same thing. If, however, you pull on both, you're still only lifting x mass (you can see the weights) yet somehow each cable is still requiring y force.

See the pulley on the right:



The forces in the cables are equal, and stay the same no matter if you pull one of them or both.