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]

Moby Thesaurus II by Grady Ward, 1.0:

325 Moby Thesaurus words for "sway":
   acme, administration, affect, alternate, amplitude, angle,
   angle off, angularity, argue into, ascend, ascendancy, authority,
   authorization, back and fill, bank, be-all and end-all, bear off,
   bear reign, bend, bias, blue ribbon, blunder, bob, bobble,
   break down, bring, bring over, bring round, bring to reason, cant,
   captivate, careen, career, carry, cave in, championship, charisma,
   charm, civil government, claws, climb, clout, clutches, coggle,
   collapse, color, command, con, conduct, consequence, control,
   convince, credit, crook, dangle, decide, decline, deflect, descend,
   determine, deviate, dip, direct, direction, directorship,
   discipline, dispensation, dispose, disposition, distort, divagate,
   diverge, divert, dominance, domination, dominion, draw over, drop,
   ebb and flow, effect, effectiveness, eminence, empery, empire,
   enchantment, engage, enlist, esteem, expanse, fall, fall away,
   fall in, fall off, falter, favor, first place, first prize,
   flounce, flounder, fluctuate, flutter, force, form of government,
   founder, gain, gain over, get, get to do, go downhill,
   go through phases, go uphill, good feeling, govern, governance,
   government, grade, grasp, grip, hand, hands, headship, heave,
   hegemony, height, highest, hobbyhorse, hold, hook, hook in,
   imperium, importance, impress, incidental power, inclination,
   incline, induce, influence, influentiality, insinuation, inspire,
   interest in, iron hand, jaundice, jurisdiction, keel, kingship,
   labor, lead, leadership, lean, leaning, leaning tower, leverage,
   librate, libration, list, lordship, lurch, lure, magnetism,
   make heavy weather, manage, management, mastership, mastery,
   maximum, might, moment, most, move, ne plus ultra, new high,
   nutate, oblique, oscillate, outtalk, overrule, oversight, palms,
   paramountcy, pendulate, personality, persuade, persuasion, pitch,
   pitch and plunge, pitch and toss, plunge, political organization,
   polity, potency, pound, power, predispose, predominance, prejudice,
   prejudice against, prejudice the issue, preponderance, prepossess,
   presidency, pressure, prestige, prevail on, prevail upon,
   prevail with, primacy, procure, prompt, purchase, raj, rake, range,
   reach, rear, record, reel, regime, regimen, regnancy, regulation,
   reign, repute, resonate, retreat, ring the changes, rise, rock,
   roll, rule, rule over, say, scend, scope, seesaw, seethe, sell,
   sell one on, shake, sheer, shelve, shift, shuffle, sidle, skew,
   slant, slope, slue, soften up, sovereignty, spread, stagger,
   stretch, strike, strings, struggle, stumble, suasion,
   subtle influence, suggestion, supervision, supremacy, swag, sweep,
   swerve, swing, swinging, system of government, talk into,
   talk over, talons, teeter, teeter-totter, tempt, tend,
   thrash about, tilt, tinge, tip, tone, top spot, topple,
   topple down, topple over, toss, toss and tumble, toss and turn,
   totter, touch, tower of Pisa, tumble, turn, twist, undulate,
   upper hand, uprise, vacillate, vary, veer, vibrate, volutation,
   wag, waggle, wallop, wallow, wangle, wangle into, warp, wave,
   waver, wax and wane, wear down, wear the crown, weave, weigh with,
   weight, welter, whip hand, wield the scepter, win, win over,
   wobble, work, yaw, zenith