"fee for membership," 1660s, plural of due (n.) in the sense "payment legally due or obligatory" (1540s). To pay (one's) dues in the figurative sense "undergo hardships to gain experience" is from 1943.
1570s, "endeavor to gain the favor of by amorous attention," also "solicit, seek to win or attract," from court (n.), based on the sorts of behavior associated with royal courts. Related: Courted; courting.
c. 1600, "action of seeking or endeavoring to gain what another is endeavoring to gain at the same time," from Late Latin competitionem (nominative competitio) "rivalry," in classical Latin "agreement," noun of action from past participle stem of competere (see compete).
Meaning "a contest for something, a trial of skill as a test of superiority or fitness" is from 1610s. Sense of "rivalry in the marketplace" attested from 1793; that of "entity or entities with which one competes" is from 1961, especially in business.