1650s, "to fondle, caress, indulge, make a pet of," from a noun (1570s) meaning "lamb brought up as a pet" (applied to persons from 1590s), of uncertain origin. Perhaps [Skeat] from Old English cot-sæta "one who dwells in a cot" (see cote (n.) + sit (v.)). Related: Coseted; coseting. Compare German Hauslamm, Italian casiccio.
"attentive, devoted, constant in application," 1530s, from Latin assiduus "attending; continually present, incessant; busy; constant," from assidere/adsidere "to sit down to, sit by" (thus "be constantly occupied" at one's work); from ad "to" (see ad-) + sedere "to sit," from PIE root *sed- (1) "to sit." The word acquired a taint of "servile" in 18c. Related: Assiduously; assiduousness.
"be set over others, have place of authority, direct and control," 1610s, from French présider "preside over, govern" (15c.), from Latin praesidere "stand guard; superintend," literally "sit in front of," from prae "before" (see pre-) + sedere "to sit," from PIE root *sed- (1) "to sit." Usually denoting temporary superintendence or direction.
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.