1520s, "overthrown, routed, defeated, conquered" (now obsolete in this sense), from Latin profligatus "destroyed, ruined, corrupt, abandoned, dissolute," past participle of profligare "to cast down, defeat, ruin," from pro "down, forth" (see pro-) + fligere "to strike" (see afflict).
The main modern meaning "recklessly extravagant" is attested by 1779, via the notion of "ruined in morals, abandoned to vice" (1640s, implied in a use of profligation, an obsolete word attested from mid-15c. but first in a sense of "elimination, banishment"). Related: Profligately. As a noun, "one who has lost all regard for good principles," from 1709.