to weep aloud: to cry out in audible grief, mourning, or distress
This is the loud, unmistakable weeping of someone overcome by sorrow. It is not a quiet welling of tears but crying you can hear: the sobbing of mourners at a deathbed, the bitter weeping of Peter after he denied Jesus, the wailing of widows over a body being prepared for burial. Wherever the Gospels want to show real grief breaking out into the open, this is the word they reach for.
The same crying covers a wide range of occasions. It is the grief of the bereaved, but also the broken weeping of remorse, the cry of the poor and hungry whom Jesus calls blessed, and the lament of the rich and comfortable who are warned that their laughter will turn to tears. In Revelation it becomes the wailing of merchants and kings as they watch the city that made them rich go up in smoke.
The word can stand on its own (someone simply weeps) or take an object (someone weeps for or over a person or place). Rachel weeps for her children, Jesus weeps over Jerusalem, and the world weeps over fallen Babylon. The crying is the same; what differs is only whether the text names the one being wept for.
Across all these scenes the action is one and the same: sorrow that refuses to stay silent. Translators reach for weep, cry, mourn, or wail depending on how violent the grief is, but each is rendering this single picture of audible, heartfelt crying.