The Collaborative International Dictionary of English v.0.48:

Preponderance \Pre*pon"der*ance\, Preponderancy
\Pre*pon"der*an*cy\, n. [Cf. F. pr['e]pond['e]rance.]
   1. The quality or state of being preponderant; superiority or
      excess of weight, influence, or power, etc.; an
      outweighing.
      [1913 Webster]

            The mind should . . . reject or receive
            proportionably to the preponderancy of the greater
            grounds of probability.               --Locke.
      [1913 Webster]

            In a few weeks he had changed the relative position
            of all the states in Europe, and had restored the
            equilibrium which the preponderance of one power had
            destroyed.                            --Macaulay.
      [1913 Webster]

   2. (Gun.) The excess of weight of that part of a canon behind
      the trunnions over that in front of them.
      [1913 Webster]

WordNet (r) 3.0 (2006):

preponderance
    n 1: superiority in power or influence; "the preponderance of
         good over evil"; "the preponderance of wealth and power"
    2: a superiority in numbers or amount; "a preponderance of
       evidence against the defendant" [syn: preponderance,
       prevalence]
    3: exceeding in heaviness; having greater weight; "the least
       preponderance in either pan will unbalance the scale"

Moby Thesaurus II by Grady Ward, 1.0:

98 Moby Thesaurus words for "preponderance":
   accomplishment, advantage, ascendance, ascendancy, ascendant,
   authority, balance of power, bulk, charisma, charm, clout,
   consequence, control, credit, deanship, dominance, dominancy,
   domination, dominion, effect, eminence, eminent domain,
   enchantment, esteem, excellence, favor, force, good feeling,
   greatness, hegemony, hold, importance, incidental power,
   incomparability, influence, influentiality, inimitability,
   insinuation, lead, leadership, leverage, magnetism, majority, mass,
   masterdom, mastery, moment, more than half, most, one-upmanship,
   overlordship, personality, persuasion, plurality, potency, power,
   precedence, predominance, predominancy, predomination, preeminence,
   preponderancy, prepotence, prepotency, prerogative, pressure,
   prestige, primacy, principality, priority, privilege, purchase,
   reign, repute, right-of-way, rule, say, seniority, skill,
   sovereignty, strength, suasion, subtle influence, success,
   suggestion, superiority, supremacy, suzerainship, suzerainty, sway,
   the greatest number, transcendence, transcendency, upper hand,
   virtuosity, weight, weightiness, whip hand