"ruse, deception," 1937, from earlier adjectival meaning "assumed, feigned" (1620s), a figurative extension of the verbal phrase on the notion of putting on costumes or disguises. To put on (v.), of clothes, garments, etc., is by early 15c.; see from put (v.) + on (adv.). Hence "clothe, cover, assume as covering" (mid-15c.) and "assume the garb or appearance of" (real or feigned), 1520s. The expression put (someone) on "play a trick on, deceive" (by 1958) seems to be a back-formation from the noun.
1640s, "continue to advance," also "manage, be engaged in," from carry (v.) + on (adv.). The meaning "conduct oneself in a wild and thoughtless manner" is by 1828. Carryings-on is from 1660s as "questionable doings," from 1866 as "riotous behavior." As an adjective, carry-on, in reference to luggage that may be brought into the passenger compartment of an airliner, is attested by 1965.