late 15c., "to divert the attention, beguile, delude," from Old French amuser "fool, tease, hoax, entrap; make fun of," literally "cause to muse" (as a distraction), from a "at, to" (from Latin ad, but here probably a causal prefix) + muser "ponder, stare fixedly" (see muse (v.)).
Original English senses obsolete; meaning "divert from serious business, tickle the fancy of" is recorded from 1630s, but through 18c. the primary meaning was "deceive, cheat" by first occupying the attention. "The word was not in reg. use bef. 1600, and was not used by Shakespere" [OED]. Bemuse retains more of the original meaning. Greek amousos meant "without Muses," hence "uneducated."
1640s, "diversion of attention," especially in military actions, from French amusement, noun of action from amuser (see amuse).
And because all bold and irreverent Speeches touching matters of high nature, and all malicious and false Reports tending to Sedition, or to the Amusement of Our People, are punishable ... (etc.) [Charles II, Proclamation of Oct. 26, 1688]
Meaning "a pastime, play, game, anything which pleasantly diverts the attention" (from duty, work, etc.) is from 1670s, originally depreciative; meaning "pleasurable diversion" attested from 1690s. Amusement hall is from 1862; amusement park first recorded 1897.
c. 1400, "to take pleasure, to amuse oneself," from Old French desporter, deporter "to divert, amuse, please, play; to seek amusement," literally "carry away" (the mind from serious matters), from des- "away" (see dis-) + porter "to carry," from Latin portare "to carry" (from PIE root *per- (2) "to lead, pass over"). Compare disport (v.), which is the older form.
Restricted sense of "amuse oneself by active exercise in open air or taking part in some game" is from late 15c. Meaning "to wear" is from 1778. Related: Sported; sporting.
late 14c., disporten, "to divert (from sadness or ennui), cheer, amuse gaily," from Anglo-French disporter "divert, amuse," Old French desporter "to seek amusement," literally "carry away" (the mind from serious matters), from des- "away" (see dis-) + porter "to carry," from Latin portare "to carry" (from PIE root *per- (2) "to lead, pass over").
Compare disporter "a minstrel or jester" (early 15c.), also Latin deportare "to carry away, transport," in Medieval Latin also "divert, amuse." For a similar sense evolution, compare distract, divert, transport (v.). Intransitive sense of "to play, sport" is from late 14c.