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.
      [1913 Webster]

   2. Hence, to lament; to grieve.
      [1913 Webster]

            He sighed deeply in his spirit.       --Mark viii.
                                                  12.
      [1913 Webster]

   3. To make a sound like sighing.
      [1913 Webster]

            And the coming wind did roar more loud,
            And the sails did sigh like sedge.    --Coleridge.
      [1913 Webster]

            The winter winds are wearily sighing. --Tennyson.
      [1913 Webster]

   Note: An extraordinary pronunciation of this word as
         s[imac]th is still heard in England and among the
         illiterate in the United States.
         [1913 Webster]