[rephael (OP)]

Why would this Perpetual Machine not work?

Water goes up the capillary tube on the right. It is transferred from the tube to the sponge(the sponge's adhesive is stronger than the tube's) The left side of the wheel is heavier than the right side due to it having heavy wet sponges. The metal ball squeezes the water out of the sponge on the right side of the wheel. The water returns to the bottom container and the process continues.

Why would this machine stop?

[alancalverd]

Bring me a working model. I have investment funds, engineering and business expertise available. Just don't tell anyone else how you did it. 

[Kryptid]

Looks like basically the same idea as this:

In principle, it takes the exact same amount of energy to lift mass against gravity as you would get when it falls. As such, if you could somehow construct a device that had absolutely no losses to friction, vibration or other sources, it could run forever (or at least until the materials that it is constructed out of break down). As soon as you try to draw power from such a device to do work, it would run down. Noether's theorem won't let machines like that do unlimited work.

[Bored chemist]

We know it's impossible without even needing to see the way you plan to do it.
https://en.wikipedia.org/wiki/Noether%27s_theorem

[Deecart]

Why would this machine stop?

Why would it even start ?
The design you propose drop water centered at the top of the wheel.
If you had sponge here that could receive water, both sponges, left and right of the top would receive water, so no water more on one or other side.

Looks like basically the same idea as this:

This design could work more likely.
But why will it not work either ?
I have tried to understand the flaw and i have perhaps some indication : A sponge is a capillar system too.
If water climb in the tube, why would water go downwards in the sponge ? (same principe but other behavior ? ? ?)

An other problem.
If you take two pieces of wet sponges, you need some force to separate them due to the capillarity forces.