Etymology
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bight (n.)
Old English byht "bend, angle, corner," from Proto-Germanic *buhtiz (source also of Middle Low German bucht, German Bucht, Dutch bocht, Danish bught "bight, bay"), from PIE root *bheug- "to bend," with derivatives referring to bent, pliable, or curved objects. Sense of "long, narrow indentation on a coastline" is from late 15c.
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bout (n.)
1540s, "a roundabout way" (obsolete), from Middle English bught, probably from an unrecorded Old English variant of byht "a bend," from Proto-Germanic *bukhta- (see bight (n.)). Sense evolved from "a circuit of any kind" (as of a plow) to "a round at any kind of exercise" (1570s), "a round at fighting" (1590s), "a fit of drinking" (1660s), "a fit of illness" (by 1938).
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*bheug- 
Proto-Indo-European root meaning "to bend," with derivatives referring to bent, pliable, or curved objects.

It forms all or part of: akimbo; bagel; bight; bog; bow (v.) "to bend the body;" bow (n.1) "weapon for shooting arrows;" bow (n.2) "front of a ship;" bowsprit; buxom; elbow.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhujati "bends, thrusts aside;" Old English bugan, German biegen, Gothic biugan "to bend;" Old High German boug, Old English beag "a ring."
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sinus (n.)
"hollow curve or cavity in the body," early 15c., from Medieval Latin sinus, from Latin sinus "bend, fold, curve, a bent surface; a bay, bight, gulf; a fold in land;" also "fold of the toga about the breast," hence "bosom," and figuratively "love, affection, intimacy; interior, inmost part;" of unknown origin.
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