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Build a small balance beam with two containers on each end.
Place the object of unknown weight in one of the containers. Add water to the other container until a ballance is achived. Measure the volume of water required to achive the balance and you have your weight. 1 litre = 1 kilogram, 1 mililitre = 1 miligram.
If one was interested in collecting imperial measurements you could try off setting the water container on the beam to perform the conversion. Weigh side 2.2 times longer than the water catchment side.( I haven't tried this, but it should work...

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