Old English hebban "to lift, raise; lift up, exalt" (class VI strong verb; past tense hof, past participle hafen), from Proto-Germanic *hafjan (cf. Old Norse hefja, Dutch heffen, German heben, Gothic hafjan "to lift, raise"), from PIE *kap-yo-, from root *kap- "to grasp" (see capable).
Related to Old English habban "to hold, possess." Intransitive use by c.1200. Meaning "to throw" is from 1590s. 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).
1570s, from heave (v.).
A shelter: Heave. Any shelter used by a policeman to avoid the elements (1950s+ Police)
To vomit; barf (1868+)