[WayneS]

It is assumed that a kilogram is a kilogram no matter where or when it is measured.

Really? Who assumes that?

[Swordmaker]

It is assumed that a kilogram is a kilogram no matter where or when it is measured.

Really? Who assumes that?

The author is referring to kilograms of mass, not weight, and the accepted axiom is that no matter where one measures that mass, the mass remains the same. However, we know that there conditions in which that mass changes, so it is now obvious that axiom is untrue.