c. 1300, "an ordinance to fix the amount of a payment or tax," from Old French sise, shortened form of assise "session, assessment, regulation, manner," noun use of fem. past participle of asseoir "to cause to sit," from Latin assidere/adsidere "to sit beside" (and thus to assist in the office of a judge), "sit with in counsel or office," from ad "to" (see ad-) + sedere "to sit," from PIE root *sed- (1) "to sit."
Probably a misdivision of l'assise as la sise. The sense of "extent, amount, volume, magnitude" (c. 1300) is from the notion of regulating something by fixing the amount of it (weights, food portions, etc.). Specific sense of "set of dimensions of a manufactured article for sale" is attested from 1590s.