1776, "a display," from the verbal phrase, attested by 1793 as "make a conspicuous and obvious display;" see show (v.) + off (adv.). From 1801 as "a deliberate and ostentatious display;" in reference to the person who makes such a display, attested from 1924. The noun showing-off "ostentatious display" is from 1874.
1570s, "procrastinating," from the verbal phrase; see off (adv.) + put (v.). Meaning "creating an unfavorable impression" is attested by 1894. To put off is attested from late 14c. as "defer, postpone, delay;" 1560s as "dismiss by an evasion;" 1610s as "divert from one's purpose." As a noun, put-off in the sense of "an excuse for evasion or delay" is attested from 1540s.