how do they get counter-weights onto high cranes?
The top section of a tower crane, including the cab, boom, and counterbalance, is erected on the crane's base, using a portable crane. After that, there is a mechanism on the tower crane that jacks up the top and allows another tower section to be inserted under it to increase the crane's height.
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The crane itself hoists them. Suppose a crane is rated to support X tons, then the optimal counter weight would be X/2 tons, an the crane has to be designed to support an imbalance of X/2 tons. If the operational crane is not lifting anything, then it has to support its unbalanced counter weight, and if it lifts its maximum load, then it has to stand an unbalanced load of (again) X/2 -- the other half of the load is balanced by the counterweight. Therefore the crane is capable of hoisting its own counterweight as an unbalanced load. It is then secured in place and the crane can then start operating to its rated maximum lifting capability.
This is overkill. 50 tons from 1 foot or 1 ton from 50 foot would do the job. Arguably it would be more humane, but humane execution was the express intent of the guillotine. Didn't stop it being widely reviled. You might be interested in the wikipedia article, Execution by Elephant, the nearest to what you suggest that has actually been used.
