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:

Sway \Sway\ (sw[=a]), v. i.
   1. To be drawn to one side by weight or influence; to lean;
      to incline.
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            The balance sways on our part.        --Bacon.
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   2. To move or swing from side to side; or backward and
      forward.
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   3. To have weight or influence.
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            The example of sundry churches . . . doth sway much.
                                                  --Hooker.
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   4. To bear sway; to rule; to govern.
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            Hadst thou swayed as kings should do. --Shak.
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The Collaborative International Dictionary of English v.0.48:

Sway \Sway\, n.
   1. The act of swaying; a swaying motion; the swing or sweep
      of a weapon.
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            With huge two-handed sway brandished aloft.
                                                  --Milton.
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   2. Influence, weight, or authority that inclines to one side;
      as, the sway of desires. --A. Tucker.
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   3. Preponderance; turn or cast of balance.
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            Expert
            When to advance, or stand, or turn the sway
            Of battle.                            --Milton.
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   4. Rule; dominion; control. --Cowper.
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            When vice prevails, and impious men bear sway,
            The post of honor is a private station. --Addison.
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   5. A switch or rod used by thatchers to bind their work.
      [Prov. Eng.] --Halliwell.
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   Syn: Rule; dominion; power; empire; control; influence;
        direction; preponderance; ascendency.
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WordNet (r) 3.0 (2006):

sway
    n 1: controlling influence
    2: pitching dangerously to one side [syn: rock, careen,
       sway, tilt]
    v 1: move back and forth or sideways; "the ship was rocking";
         "the tall building swayed"; "She rocked back and forth on
         her feet" [syn: rock, sway, shake]
    2: move or walk in a swinging or swaying manner; "He swung back"
       [syn: swing, sway]
    3: win approval or support for; "Carry all before one"; "His
       speech did not sway the voters" [syn: carry, persuade,
       sway]
    4: cause to move back and forth; "rock the cradle"; "rock the
       baby"; "the wind swayed the trees gently" [syn: rock,
       sway]