sizeyoudaoicibaDictYouDict[size 词源字典]
size: [13] The etymological notion underlying size is of ‘settling’ something, of fixing an amount. The word is a curtailed version of assize, which went back ultimately to Latin assidēre, literally ‘sit beside someone’. By the time it reached English, via Old French, it had acquired connotations of ‘sitting down to make a judgment on something’, such as a law case (hence the meaning of English assize).

Other matters decided on in this way included the standardization of amounts (of taxes, for example, or food), and this led to the word size being used for ‘dimension’. Size ‘gum’ [15] may be the same word, but the nature of the relationship between the two is unclear.
=> assize, sit[size etymology, size origin, 英语词源]
size (n.)youdaoicibaDictYouDict
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.
size (v.)youdaoicibaDictYouDict
c. 1400, "to regulate," from size (n.). Meaning "to make of a certain size" is from c. 1600; that of "to classify according to size" is first attested 1630s. Verbal phrase size up "estimate, assess" is from 1847 and retains the root sense of size (n.). Related: Sized; sizing.