size (n.)

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.

size (v.)

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.

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Definitions of size from WordNet
size (n.)
the physical magnitude of something (how big it is);
a wolf is about the size of a large dog
size (n.)
the property resulting from being one of a series of graduated measurements (as of clothing);
he wears a size 13 shoe
size (n.)
any glutinous material used to fill pores in surfaces or to stiffen fabrics;
size gives body to a fabric
Synonyms: sizing
size (n.)
the actual state of affairs;
she hates me, that's about the size of it
that's the size of the situation
Synonyms: size of it
size (n.)
a large magnitude;
he blanched when he saw the size of the bill
the only city of any size in that area
size (v.)
cover or stiffen or glaze a porous material with size or sizing (a glutinous substance);
size (v.)
sort according to size;
size (v.)
make to a size; bring to a suitable size;
size (adj.)
(used in combination) sized;
the economy-size package
average-size house