The Collaborative International Dictionary of English v.0.48:

Equalize \E"qual*ize\, v. t. [imp. & p. p. Equalized; p. pr. &
   vb. n. Equalizing.] [Cf. F. ['e]galiser.]
   1. To make equal; to cause to correspond, or be like, in
      amount or degree as compared; as, to equalize accounts,
      burdens, or taxes.
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            One poor moment can suffice
            To equalize the lofty and the low.    --Wordsworth.
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            No system of instruction will completely equalize
            natural powers.                       --Whately.
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   2. To pronounce equal; to compare as equal.
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            Which we equalize, and perhaps would willingly
            prefer to the Iliad.                  --Orrery.
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   3. To be equal to; equal; to match. [Obs.]
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            It could not equalize the hundredth part
            Of what her eyes have kindled in my heart. --Waller.
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   Equalizing bar (Railroad Mach.), a lever connecting two
      axle boxes, or two springs in a car truck or locomotive,
      to equalize the pressure on the axles.
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WordNet (r) 3.0 (2006):

equalize
    v 1: compensate; make the score equal [syn: equalize,
         equalise, get even]
    2: make equal, uniform, corresponding, or matching; "let's
       equalize the duties among all employees in this office"; "The
       company matched the discount policy of its competitors" [syn:
       equal, match, equalize, equalise, equate]

Moby Thesaurus II by Grady Ward, 1.0:

97 Moby Thesaurus words for "equalize":
   accommodate, accord, adapt, adjust, adjust to, align, assimilate,
   assimilate to, attune, balance, cancel, compensate, coordinate,
   counterbalance, counterpoise, countervail, cut to, dab, damp, drag,
   dress, dub, equal, equate, equilibrize, even, even up, fell, fit,
   fix, flatten, flush, gear to, grade, grease, harmonize, harrow,
   homogenize, homologate, homologize, integrate, key to, lay,
   lay down, lay flat, lay level, lay low, lay out, level, lubricate,
   make plumb, make uniform, match, measure, mow, normalize, oil,
   plane, planish, plaster, poise, proportion, proportionate,
   put in tune, rase, raze, reconcile, rectify, regularize, regulate,
   right, roll, roll flat, set, set right, shave, similarize, smooth,
   smooth down, smooth out, smoothen, square, stabilize, standardize,
   steamroll, steamroller, stereotype, strike a balance, symmetrize,
   sync, synchronize, tailor, trim to, true, true up, tune,
   uniformize