Merriam-Webster's Collegiate® Dictionary, 11th Edition
SIGH
I. verb
Etymology: Middle English sihen, alteration of sichen, from Old English sīcan; akin to Middle Dutch versiken to sigh
Date: 13th century
intransitive verb to take a deep audible breath (as in weariness or relief), to make a sound like sighing , grieve , yearn , transitive verb to express by sighs, to utter sighs over ; mourn , sigher noun
II. noun
Date: 14th century
an often involuntary act of sighing especially when expressing an emotion or feeling (as weariness or relief), the sound of gently moving or escaping air