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Jesus,
My humble opinion. If you have two equal weights (forget the monkey) tied to the ends of a real (i.e. with weight) rope and hang them over a frictionless pulley, they will be in equilibrium ONLY at equal height. This is because the weight of the rope is also acted upon by gravity, so on each side you have the weight of the rope+weight and they must be at equal height to balance. If you pull down on the left side and hold, you now have more weight on the left due to more rope and when you let go, the left side will fall.
I think the comprehension problem come from the fact that we find it hard to picture a weightless rope. But if there is a weightless rope and the weights are at different heights, they would still be balanced with the same weight pulling down on both sides. This seems odd, but I can think of no reason why this wouldn't occur - gravity acts on both weights equally and with no other weight, they should not have to be equal distance. With a weightless rope if you pull down on the left side, hold, then release, you still have equal forces on both sides and the weights will not move - at least that is my belief.
BW
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