[baby]

Interesting, because I think about it the other way: the offset tells you between which power of two you're in:

* [2^-127, 2^-126] * ... * [1, 2] * [2, 2^2] * [2^2, 2^3] * ... * [2^128, 2^129]

and the window tells you where you are in this "window". You have 8 bits to figure out where you are in there, so it's obvious that you have much more precision if you are in the window [1, 2] than in the window [2^128, 2^129]