bate (v.1)

c. 1300, "to alleviate, allay;" mid-14c., "suppress, do away with;" late 14c., "to reduce; to cease," a shortening of abate (q.v.). Now only in phrase bated breath (subdued or shortened breathing, from fear, passion, awe, etc.), which was used by Shakespeare in "The Merchant of Venice" (1596).

bate (v.2)

c. 1300, "to contend with blows or arguments," from Old French batre "to hit, beat, strike" (11c., Modern French battre), from Late Latin battere, from Latin batuere "to beat, knock" (see batter (v.)). In falconry, "to beat the wings impatiently and flutter away from the perch." Figurative sense of "to flutter downward" attested from 1580s.

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Definitions of bate from WordNet

bate (v.)
moderate or restrain; lessen the force of;
He bated his breath when talking about this affair
bate (v.)
flap the wings wildly or frantically; used of falcons;
bate (v.)
soak in a special solution to soften and remove chemicals used in previous treatments;
bate hides and skins