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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" (see assize), 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.
To estimate or assess: How do you size up his chances? (1847+)