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An average man 2 metres tall ideal weight is between 74 and 100.4 kg [http://www.nhs.uk/tools/pages/healthyweightcalculator.aspx?tag=], the 'perfect' weight would be 87.2 kg. The average (or ideal) weight for a boy of 4 years is 16.3 kg with a height of 1.023 m.[http://www.disabled-world.com/artman/publish/height-weight-teens.shtml] Let's say 16 kg for 1 m. 16x8=128kg (Theoretical 'ideal' weight of man twice the height of a 1m boy.)
I would say that's not too far out (especially from the upper limit of the 'ideal' weight) from the cubic relationship. I didn't expect it to be a perfect match. It's almost as good a fit as a square relationship, which would give a weight or 64kg for a 2m-tall man.
In response to bhg481 (which I had put as best answer before I thought about it some more), OK the human body is more like a cylinder than a sphere, so why not divide the weight by the square of the waist measurement, rather than the square of the height? The mass of a cylinder would be proportional to the height (for a constant radius), not the square of the height.