The A0 being 1m^2 is important because paper weight is given in gsm - grams per square metre.
Thus when calculating postage weight by counting the number of sheets you can calculate that, for example, the weight of one A4 sheet is 1/16 the gsm of the paper - 1/(2^4).
In order to figure out the actual mass of a sheet of U.S. paper from the reported basis weight, you must know how many sheets of paper were in the "basis ream" and what dimensions they were. The basis ream sheet dimensions may have nothing to do with your final sheet of paper, and the number of sheets varies too.
Thus when calculating postage weight by counting the number of sheets you can calculate that, for example, the weight of one A4 sheet is 1/16 the gsm of the paper - 1/(2^4).