The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, v. i. [imp. & p. p. Sighed; p. pr. & vb. n.
   Sighing.] [OE. sighen, si?en; cf. also OE. siken, AS.
   s[imac]can, and OE. sighten, si?ten, sichten, AS. siccettan;
   all, perhaps, of imitative origin.]
   1. To inhale a larger quantity of air than usual, and
      immediately expel it; to make a deep single audible
      respiration, especially as the result or involuntary
      expression of fatigue, exhaustion, grief, sorrow, or the
      like.
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   2. Hence, to lament; to grieve.
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            He sighed deeply in his spirit.       --Mark viii.
                                                  12.
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   3. To make a sound like sighing.
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            And the coming wind did roar more loud,
            And the sails did sigh like sedge.    --Coleridge.
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            The winter winds are wearily sighing. --Tennyson.
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   Note: An extraordinary pronunciation of this word as
         s[imac]th is still heard in England and among the
         illiterate in the United States.
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The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, v. t.
   1. To exhale (the breath) in sighs.
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            Never man sighed truer breath.        --Shak.
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   2. To utter sighs over; to lament or mourn over.
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            Ages to come, and men unborn,
            Shall bless her name, and sigh her fate. --Pior.
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   3. To express by sighs; to utter in or with sighs.
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            They . . . sighed forth proverbs.     --Shak.
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            The gentle swain . . . sighs back her grief.
                                                  --Hoole.
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The Collaborative International Dictionary of English v.0.48:

Sigh \Sigh\, n. [OE. sigh; cf. OE. sik. See Sigh, v. i.]
   1. A deep and prolonged audible inspiration or respiration of
      air, as when fatigued or grieved; the act of sighing.
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            I could drive the boat with my sighs. --Shak.
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   2. Figuratively, a manifestation of grief; a lan?ent.
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            With their sighs the air
            Frequenting, sent from hearts contrite. --Milton.
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WordNet (r) 3.0 (2006):

sigh
    n 1: an utterance made by exhaling audibly [syn: sigh,
         suspiration]
    2: a sound like a person sighing; "she heard the sigh of the
       wind in the trees"
    v 1: heave or utter a sigh; breathe deeply and heavily; "She
         sighed sadly" [syn: sigh, suspire]
    2: utter with a sigh