
Cry one's eyes out
Sob one's eyes out / Cry one's heart out / Run out of tears / Weep a flood of tears / Cry like a fountain / Be beyond crying

Piangere a dirotto 
Piangere a calde lacrime / Consumarsi gli occhi dal piangere / Piangere come un vitello / Piangere come un vitellino / Piangere come una vite tagliata
Sob one's eyes out / Cry one's heart out / Run out of tears / Weep a flood of tears / Cry like a fountain / Be beyond crying

Piangere a dirotto 
Piangere a calde lacrime / Consumarsi gli occhi dal piangere / Piangere come un vitello / Piangere come un vitellino / Piangere come una vite tagliata
Meanings
Fig.: to sob long and bitterly
Examples
It was a big scandal: Lady B was seen in the ladies' restroom sobbing her eyes out for no apparent reason
È stato un grosso scandalo: Lady B È stata vista nel bagno delle signore piangere a dirotto senza una ragione apparente
The little girl was desperate and crying her heart out because her puppy got lost. Luckily a nice neighbor found him and brought him back to her
La povera bambina era disperata e piangeva a calde lacrime perché il suo cucciolo si era perso. Fortunatamente un vicino lo ha trovato e glielo ha riportatoOrigin
The first written appearance of this expression in English is to be found in Cervantes' DON QUIXOTE (1604). Don Quixote asks Sancho to witness some of his acts of penance, and Sancho replies: "Good sir, as you love me, don't let me stay to see you naked; 'twill grieve me so to the heart, that I shall cry my eyes out"