means To release a long, audible breath, usually expressing tiredness, relief, longing, or resignation.

from From Middle English sighen, likely a back-formation from the old past tense of siken, meaning 'to sigh.' It traces to Old English sīcan, of the same sense — a word that's essentially imitative, the spelling itself a little exhalation. Cousins ripple through the Germanic family, and the gh, once pronounced as a soft throaty rasp, has long since fallen silent, leaving only the breath behind.