Etymology
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heave (n.)
1570s, from heave (v.). Meaning "a dismissal" is from 1944.
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heave (v.)
Old English hebban "to lift, raise; lift up, exalt" (class VI strong verb; past tense hof, past participle hafen), from Proto-Germanic *hafjan (source also of Old Norse hefja, Dutch heffen, German heben, Gothic hafjan "to lift, raise"), from PIE *kap-yo-, from root *kap- "to grasp." The sense evolution would be "to take, take hold of," thence "lift."

Related to have (Old English habban "to hold, possess"). Meaning "to throw" is from 1590s. Nautical meaning "haul or pull" in any direction is from 1620s. Intransitive use from early 14c. as "be raised or forced up;" 1610s as "rise and fall with alternate motion." Sense of "retch, make an effort to vomit" is first attested c. 1600. Related: Heaved; heaving. Nautical heave-ho was a chant in lifting (c. 1300, hevelow).
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hoove 
cattle disease, 1840, from alternative past tense form of heave.
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heft (n.)
mid-15c., "weight, heaviness, quality of weight," from heave (v.) on analogy of thieve/theft, weave/weft, etc. Also influenced by heft, obsolete past participle of heave.
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hove (v.2)
"to rise up, to swell," 1590s, evidently from heave (v.), perhaps from its past tense form hove.
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upheaval (n.)
1834 in reference to convulsions in society; 1836 in geology, from verb upheave (c. 1300, from up (adv.) + heave (v.)) + -al (2). Similarly formed verbs are Old Frisian upheva, Old High German ufhevan, German aufheben.
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behoof (n.)
c. 1200, "use, benefit, advantage," from Old English *bihof "advantage, utility" (implied by bihoflic "useful," and compare behoove), from Proto-Germanic *bi-hof "that which binds, requirement, obligation" (source also of Old Frisian bihof "advantage," Dutch behoef, Middle High German bihuof "useful thing," German Behuf "benefit, use, advantage," Danish behov "need, necessity"). In the common Germanic compound, the first element, likely intensive, is cognate with be- and the second with Old English hof, past tense of hebban "to raise" (see heave (v.)). The original sense is perhaps, then, "taking up (for oneself)."
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haff (n.)

also haaf, Baltic lagoon, separated from open sea by a sandbar, German, from Middle Low German haf "sea," from Proto-Germanic *hafan (source also of Old Norse haf, Swedish haf "the sea," especially "the high sea," Danish hav, Old Frisian hef, Old English hæf "sea"), perhaps literally "the rising one," and related to the root of heave, or a substratum word from the pre-Indo-European inhabitants of the coastal regions. The same word as haaf "the deep sea," which survived in the fishing communities of the Shetland and Orkney islands.

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*kap- 

Proto-Indo-European root meaning "to grasp."

It forms all or part of: accept; anticipate; anticipation; behave; behoof; behoove; cable; cacciatore; caitiff; capable; capacious; capacity; capias; capiche; capstan; caption; captious; captivate; captive; captor; capture; case (n.2) "receptacle;" catch; catchpoll; cater; chase (n.1) "a hunt;" chase (v.) "to run after, hunt;" chasse; chasseur; conceive; cop (v.) "to seize, catch;" copper (n.2) "policeman;" deceive; emancipate; except; forceps; gaffe; haft; have; hawk (n.); heave; heavy; heft; incapacity; inception; incipient; intercept; intussusception; manciple; municipal; occupy; participation; perceive; precept; prince; purchase; receive; recipe; recover; recuperate; sashay; susceptible.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kapati "two handfuls;" Greek kaptein "to swallow, gulp down," kope "oar, handle;" Latin capax "able to hold much, broad," capistrum "halter," capere "to grasp, lay hold; be large enough for; comprehend;" Lettish kampiu "seize;" Old Irish cacht "servant-girl," literally "captive;" Welsh caeth "captive, slave;" Gothic haban "have, hold;" Old English hæft "handle," habban "to have, hold."

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hives (n.)
c. 1500 hyvis "itchy condition of the skin," origin unknown. Some writers connect it with heave because hives erupt out from the skin, but the phonetics of that are difficult to explain.
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