Etymology
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hundredweight (n.)
1540s, from hundred + weight. Commonly 100 lbs., but it could vary locally and in specific uses up to 120 lbs.
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middleweight (n.)

also middle-weight, "boxer or jockey of intermediate weight" (between a lightweight and a heavyweight), 1842, from middle (adj.) + weight (n.).

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heavyweight 
also heavy-weight, noun and adjective, 1857 of horses; 1877 of fighters; from heavy (adj.) + weight. Figuratively, in reference to importance, from 1928.
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pennyweight (n.)

unit of measure equal to the weight of one penny, Old English penega gewiht, originally the weight of a silver penny (22 grains); see penny + weight (n.).

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lightweight (adj.)
also light-weight, 1809, from the noun (1773 in horse-racing, also in pugilism), "man or animal of a certain weight prescribed by rule," from light (adj.1) + weight (n.). Figurative sense of "inconsequential" first attested 1809. The noun sense of "person of little importance or accomplishment" is from 1885.
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makeweight (n.)

also make-weight, 1690s, "small quantity of something added to make the total reach a certain weight," from make (v.) + weight. Meaning "thing or person of little account made use of" is from 1776.

MAKE WEIGHT. A small candle: a term applied to a little slender man. [Grose, "Dictionary of the Vulgar Tongue," London, 1785]

For the formation, compare makeshift, also make-sport (1610s), makegame (1762) "a laughing stock, a butt for jokes;" makebate "one who excites contentions and quarrels" (1520s); makepeace "a peace-maker, one who reconciles persons at variance" (early 13c. as a surname).

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*wegh- 

Proto-Indo-European root meaning "to go, move, transport in a vehicle."

The root wegh-, "to convey, especially by wheeled vehicle," is found in virtually every branch of Indo-European, including now Anatolian. The root, as well as other widely represented roots such as aks- and nobh-, attests to the presence of the wheel — and vehicles using it — at the time Proto-Indo-European was spoken. [Watkins, p. 96]

It forms all or part of: always; away; convection; convey; convex; convoy; deviate; devious; envoy; evection; earwig; foy; graywacke; impervious; invective; inveigh; invoice; Norway; obviate; obvious; ochlocracy; ogee; pervious; previous; provection; quadrivium; thalweg; trivia; trivial; trivium; vector; vehemence; vehement; vehicle; vex; via; viaduct; viatic; viaticum; vogue; voyage; wacke; wag; waggish; wagon; wain; wall-eyed; wave (n.); way; wee; weigh; weight; wey; wiggle.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vahati "carries, conveys," vahitram, vahanam "vessel, ship;" Avestan vazaiti "he leads, draws;" Greek okhos "carriage, chariot;" Latin vehere "to carry, convey," vehiculum "carriage, chariot;" Old Church Slavonic vesti "to carry, convey," vozŭ "carriage, chariot;" Russian povozka "small sled;" Lithuanian vežu, vežti "to carry, convey," važis "a small sled;" Old Irish fecht "campaign, journey," fen "carriage, cart;" Welsh gwain "carriage, cart;" Old English wegan "to carry;" Old Norse vegr, Old High German weg "way;" Middle Dutch wagen "wagon."

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poundage (n.)

early 15c., "tax or subsidy per pound of weight;" 1903 as "weight;" from pound (n.1) + -age.

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wey (n.)
dry goods weight of fixed amount (but varying over time and place), Old English weg "scales, balance, weight" (see weigh).
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bariatric (adj.)

"of or pertaining to obesity," 1976, from Greek baros "weight, a weight, burden," related to barys "heavy" (from PIE root *gwere- (1) "heavy") + -iatric.

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