Im sorry that I havent had the patience to read the entire flamefight before posting so I hope this is not redundant It should be obvious from reductio ad absurdum that the entire mass gain from raising a kilogram above the Earth cannot in principle reside completely in the kilogram in question Imagine that the Earth weighed one kilogram or rather that you are somehow sitting between two identical kilogram objects somewhere in space If you raise one of them by separating it from the other where does the change in mass go Theres no way of choosing Now if you make one of them heavier maybe you could argue that the majority of the mass change goes only to one of them In the limit of infinite mass you could say that all the mass change belongs to one object However the Earth does not have an infinite mass although it may be a good approximation in practice when compared with one kilogram I have the impression that Gregs point of view has a implicit geocentric assumption that should be made explicit to clarify why he assigns the change in mass to the kilogram Leaving mass aside for a moment and going back to classical physics it is basic knowledge that the potential energy change does not belong to the kilogram but to the Earthkilogram interaction Therefore the statement made in the footnote that the potential energy  and mass  the kilogram gains by rising out of Earths gravity well is independent of its position relative to an observer is simply not correct in principle The kilogram does not gain potential energythe system does