If you use a different calibration weight, you are essentially using a different unit of measurement despite calling it the same name. Thus, as long as people keep their units under control when transferring data between people, there will be no problem.
Numbers are totally arbitrary. If I say that my body weight is now 1 firakegram, then it is. And if you then use the force which my body weighs down on a scale to measure the weight of two smaller people you might find that they are 1.8 firakegrams. Weight itself is a fundamental property of an object, but how the numbers and units we use to represent it are completely arbitrary. We don’t need to know the “actual” (and we can’t know it, anyway. What units does the universe use?) weight of something as long as we know what other people mean when we give them our representations of the objects weight.
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