Tears figure highly in teaching about the Jesus Prayer as they point towards repentance and sorrow for sin. Here is one of the sayings of the Desert Fathers on the subject.
Abba Poeman said: "One who wishes to purify one's faults purifies them with tears; one who wishes to acquire the virtues acquires them with tears. Weeping is the way that the Scriptures and the Fathers give us, when they say: 'Weep!' Truly, there is no other way than this."