Webster's Revised Unabridged Dictionary · 1913

Sigh

Sigh , intransitive verb

[Old English sighen, si{not transcribed}en; compare also Old English siken, Anglo-Saxon sīcan, and Old English sighten, si{not transcribed}ten, sichten, Anglo-Saxon 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.
2.
Hence, to lament; to grieve.
He sighed deeply in his spirit. — Mark viii. 12
3.
To make a sound like sighing.
And the coming wind did roar more loud, And the sails did sigh like sedge. — Coleridge
The winter winds are wearily sighing. — Tennyson

An extraordinary pronunciation of this word as sīth is still heard in England and among the illiterate in the United States.

Sigh , transitive verb

1.
To exhale (the breath) in sighs.
Never man sighed truer breath. — Shakespeare
2.
To utter sighs over; to lament or mourn over.
Ages to come, and men unborn, Shall bless her name, and sigh her fate. — Pior
3.
To express by sighs; to utter in or with sighs.
They... sighed forth proverbs. — Shakespeare
The gentle swain... sighs back her grief. — Hoole

Sigh , noun

[Old English sigh; compare Old English 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.
I could drive the boat with my sighs. — Shakespeare
2.
Figuratively, a manifestation of grief; a lament.
With their sighs the air Frequenting, sent from hearts contrite. — Milton