How does a tension lever exert different tensions with only one mass?

See the hinge below the string? When you hang a weight on that lever, the contraption wants to rotate around that hinge. The string prevents it from rotating, but it gets stretched in doing so. The torque that the lever applies is directly proportional to the distance that a weight hang​s from the hinge, and that torque becomes tension in the string.

I think you can solve this mystery yourself by doing a free body diagram for one of the cases. I chose the 3Mg case below.

Now balance the forces and moments to find the tension $T$, as well as the pivot reaction forces $A_x$ and $A_y$ in terms of the weight $Mg$.