The Collaborative International Dictionary of English v.0.48:

Sway \Sway\ (sw[=a]), v. t. [imp. & p. p. Swayed; p. pr. & vb.
   n. Swaying.] [OE. sweyen, Icel. sveigja, akin to E. swing;
   cf. D. zwaaijen to wield, swing. See Swing, and cf. Swag,
   v. i.]
   1. To move or wield with the hand; to swing; to wield; as, to
      sway the scepter.
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            As sparkles from the anvil rise,
            When heavy hammers on the wedge are swayed.
                                                  --Spenser.
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   2. To influence or direct by power and authority; by
      persuasion, or by moral force; to rule; to govern; to
      guide.
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            The will of man is by his reason swayed. --Shak.
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            She could not sway her house.         --Shak.
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            This was the race
            To sway the world, and land and sea subdue.
                                                  --Dryden.
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   3. To cause to incline or swing to one side, or backward and
      forward; to bias; to turn; to bend; warp; as, reeds swayed
      by wind; judgment swayed by passion.
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            As bowls run true by being made
            On purpose false, and to be swayed.   --Hudibras.
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            Let not temporal and little advantages sway you
            against a more durable interest.      --Tillotson.
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   4. (Naut.) To hoist; as, to sway up the yards.
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   Syn: To bias; rule; govern; direct; influence; swing; move;
        wave; wield.
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The Collaborative International Dictionary of English v.0.48:

Swaying \Sway"ing\, n.
   An injury caused by violent strains or by overloading; --
   said of the backs of horses. --Crabb.
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Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "swaying":
   ascendant, careening, dangling, dominant, in ascendancy,
   in the ascendant, lurching, on the throne, pitching, predominant,
   prepollent, preponderant, prepotent, prevailing, reeling, regnant,
   rocking, rolling, ruling, swinging, tossing