In practice regular paper has ~80g/m^2, meaning 5 grams per sheet, meaning a ream of 500 sheets has exactly 2.5 kg.
In addition to A series, there is also B series (and C series). They all have the same aspect ratio √2
B0 is 1 metre wide, while A0 is 1 meter long. The area of B series sheets is the geometric mean of successive A series sheets. Many books are printed in size B5. When you fold A4 it fits neatly between the pages.
Letter written on A4 paper fits inside a C4 envelope, and both A4 paper and C4 envelope fit inside a B4 envelope.
The decimeter (i.e. 10cm; ⅒ of a meter) has been hiding in plain sight and fits the bill adequately. It is, however, awkward to communicate. It's about the same width as the width across an average adult's hand, so let's rebrand the decimeter as the "metric hand", or just "hand" in informal contexts.
Conveniently, there are approximately 3 metric hands in 1 foot. The error, 1.6mm per hand, is negligible, and in instances where accuracy and/or precision is at a premium you can rest safe knowing that it really does accumulate at 1.6mm per hand exactly, and not some intractable quantity like the one that comes up with approximating 1 kg as 2.2 lbs.