The Collaborative International Dictionary of English v.0.48:

Heave \Heave\ (h[=e]v), v. t. [imp. Heaved (h[=e]vd), or
   Hove (h[=o]v); p. p. Heaved, Hove, formerly Hoven
   (h[=o]"v'n); p. pr. & vb. n. Heaving.] [OE. heven, hebben,
   AS. hebban; akin to OS. hebbian, D. heffen, OHG. heffan,
   hevan, G. heben, Icel. hefja, Sw. h[aum]fva, Dan. h[ae]ve,
   Goth. hafjan, L. capere to take, seize; cf. Gr. kw`ph handle.
   Cf. Accept, Behoof, Capacious, Forceps, Haft,
   Receipt.]
   1. To cause to move upward or onward by a lifting effort; to
      lift; to raise; to hoist; -- often with up; as, the wave
      heaved the boat on land.
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            One heaved ahigh, to be hurled down below. --Shak.
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   Note: Heave, as now used, implies that the thing raised is
         heavy or hard to move; but formerly it was used in a
         less restricted sense.
         [1913 Webster]

               Here a little child I stand,
               Heaving up my either hand.         --Herrick.
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   2. To throw; to cast; -- obsolete, provincial, or colloquial,
      except in certain nautical phrases; as, to heave the lead;
      to heave the log.
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   3. To force from, or into, any position; to cause to move;
      also, to throw off; -- mostly used in certain nautical
      phrases; as, to heave the ship ahead.
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   4. To raise or force from the breast; to utter with effort;
      as, to heave a sigh.
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            The wretched animal heaved forth such groans.
                                                  --Shak.
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   5. To cause to swell or rise, as the breast or bosom.
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            The glittering, finny swarms
            That heave our friths, and crowd upon our shores.
                                                  --Thomson.
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   To heave a cable short (Naut.), to haul in cable till the
      ship is almost perpendicularly above the anchor.

   To heave a ship ahead (Naut.), to warp her ahead when not
      under sail, as by means of cables.

   To heave a ship down (Naut.), to throw or lay her down on
      one side; to careen her.

   To heave a ship to (Naut.), to bring the ship's head to the
      wind, and stop her motion.

   To heave about (Naut.), to put about suddenly.

   To heave in (Naut.), to shorten (cable).

   To heave in stays (Naut.), to put a vessel on the other
      tack.

   To heave out a sail (Naut.), to unfurl it.

   To heave taut (Naut.), to turn a capstan, etc., till the
      rope becomes strained. See Taut, and Tight.

   To heave the lead (Naut.), to take soundings with lead and
      line.

   To heave the log. (Naut.) See Log.

   To heave up anchor (Naut.), to raise it from the bottom of
      the sea or elsewhere.
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The Collaborative International Dictionary of English v.0.48:

Heaving \Heav"ing\, n.
   A lifting or rising; a swell; a panting or deep sighing.
   --Addison. --Shak.
   [1913 Webster]

WordNet (r) 3.0 (2006):

heaving
    n 1: an upward movement (especially a rhythmical rising and
         falling); "the heaving of waves on a rough sea" [syn:
         heave, heaving]
    2: breathing heavily (as after exertion) [syn: panting,
       heaving]
    3: the act of lifting something with great effort [syn: heave,
       heaving]
    4: throwing something heavy (with great effort); "he gave it a
       mighty heave"; "he was not good at heaving passes" [syn:
       heave, heaving]