To answer you, many psychological and mystical aspects of crying could be examined, but you only asked for the verses and narrations of the Prophet. So the discussion is short.
What I learned from the verses and hadiths is that the origin and cause of crying is very important. Crying out of helplessness against the oppressors is worthless but has a negative effect.
Crying before God and in worship is valuable, not crying against the oppressors and begging the servants.
In the Qur'an (Isra / Sura 17 - verse 109 and Maryam / Sura 19 - verse 58) and especially in the hadiths, crying during worship is recommended. It is said that Prophet Muhammad (peace and blessings of Allaah be upon him) sometimes cried loudly in prayer. Such a biography of the first caliphs, Abu Bakr and Umar, has also been narrated.
--Isra / Sura 17 - verse 109 >>Weeping, they fall down on their faces, and it increases them in humility. '
Interpretation >> Crying while worshiping and prostrating is valuable. Crying here is one of the blessings and effects of knowledge (in the place of the servant and God).
--Maryam / Sura 19 - verse 58 >>
They are the ones whom Allah has blessed from among the prophets of Adam’s progeny, and from [the progeny of] those We carried with Noah, and from among the progeny of Abraham and Israel, and from among those that We guided and chose. When the signs of the All-beneficent were recited to them, they would fall down weeping in prostration.
Interpretation of the verse >> It says a common feature among all the prophets who prostrated and cried when they heard the divine revelations. Crying in prostration is so valuable that God has glorified its people. «سُجَّداً وَ بُكِيًّا»
Ministerial weeping for God is a sign of growth, knowledge, success and election. وَمِمَّنْ هَدَيْنا وَ اجْتَبَيْنا
--The Messenger of God (PBUH): Crying out of fear of God is the source of salvation from hell.
Comprehensive Hadith, p. 64
--According to the Qur'an, crying out of fear of God and turning to Him in supplication is a good thing. The word "Bekaa" is used in the Qur'an and Hadith, not only in the case of man, but also in the case of angels, Satan, earth, sky, mountains, jinns, birds, etc., and this shows that the meaning of this word in the texts Islam is broader than its literal meaning of man.
According to the Qur'an, crying out of fear of God and turning to Him in supplication is a good thing. The word "Bekaa" is used in the Qur'an and Hadith, not only in the case of man, but also in the case of angels, Satan, earth, sky, mountains, jinns, birds, etc., and this shows that the meaning of this word in the texts Islam is broader than its literal meaning of man.
Ibn Fahd Hali considered crying as a sign of tenderness of heart, which is itself a sign of sincerity in the light of which obedience is achieved. He quotes a hadith from the Prophet (PBUH) in which God is considered the friend of the sad heart.
Of course, crying for worldly affairs is not only not recommended, but in some cases it is forbidden. In a hadith narrated by Ibn Hanbal from the Prophet (PBUH), worldly weeping is considered evil.
The list of favorite crying scenes in the perspective of Islam is on the following site:
بکاء ممدوح از منظر قرآن و روایات