It's an interesting word. The Online Etymology Dictionary defines it thusly:
Well, that's pretty straightforward. It means what I always thought it meant. But that last definition "to raise" looked interesting. And what does "raising" have to do with the word, "heave"? So, I had to look that up.
So, the Old English hebban "to lift, raise" worked its way from Old Norse, Dutch, German, and Goth (East Germanic tribes) back again to Old English habban "to hold, possess." Where the retching comes in I have no idea, unless it's the raising of stomach contents. I can get a handle on habban as it relates to behoove. You have to take ahold of something, possess it in order to have the benefit or advantage of it. I can also see the connection between our modern understanding of "raise" and "heave." You have to lift something up, raise it, in order to heave it, or throw it. But what's that got to do with holding or possessing something, or with something being beneficial or advantageous? That's beyond me. Then there's that pesky prefix be-. I have no idea how that fits in. Well, that's my mind's meanderings around that word. It's not exactly erudite or profound, and probably not even close to being an accurate description, but that's the way I see it.
- O.E. hebban "to lift, raise" (class VI strong verb; past tense hof, pp. hafen), from P.Gmc. *khafjanan (cf. O.N. hefja, Du. heffen, Ger. heben, Goth. hafjan), from PIE *kap- "seize;" related to O.E. habban "to hold, possess." Sense of "retch, make an effort to vomit" is first attested 1601. Nautical heave-ho was a chant in lifting.