As for wailing (niyāḥah), it is forbidden, and a chapter on it will come in the Book of Prohibitions, Allah the Exalted willing. As for weeping, there have come hadiths forbidding it and stating that the deceased is punished by the weeping of his family; but these are interpreted and are taken to refer to one who left instructions for it. The prohibition is only against weeping that involves loud lamentation (nadb) or wailing (niyāḥah). The proof for the permissibility of weeping without loud lamentation or wailing is many hadiths, among them:
رياض الصالحينAbū Zakariyyā Muḥyī al-Dīn Yaḥyā ibn Sharaf al-Nawawī١٥٣ - باب جواز البكاء على الميت بغير ندب ولا نياحة
١٥٣ - باب جواز البكاء على الميت بغير ندب ولا نياحة
﵄: - ﷺ - - ﵃ - - ﷺ - - ﷺ -
From Ibn ʿUmar (may Allah be pleased with them both): that the Messenger of Allah (peace and blessings be upon him) visited Saʿd ibn ʿUbādah, and with him were ʿAbd al-Raḥmān ibn ʿAwf, Saʿd ibn Abī Waqqāṣ, and ʿAbd Allāh ibn Masʿūd (may Allah be pleased with them). The Messenger of Allah (peace and blessings be upon him) wept, and when the people saw the weeping of the Messenger of Allah (peace and blessings be upon him), they wept too. He said: 'Do you not hear? Allah does not punish for the tears of the eye, nor for the grief of the heart, but He punishes for this — and he pointed to his tongue — or He shows mercy.' Agreed upon (al-Bukhārī and Muslim).
﵄: - ﷺ - - ﷺ -
And from Usāmah ibn Zayd (may Allah be pleased with them both): that the Messenger of Allah (peace and blessings be upon him) had his daughter's son lifted up to him while the child was dying, and the eyes of the Messenger of Allah (peace and blessings be upon him) overflowed with tears. Saʿd said to him: 'What is this, O Messenger of Allah?!' He said: 'This is a mercy which Allah the Exalted has placed in the hearts of His servants. Allah shows mercy only to those of His servants who are merciful.' Agreed upon (al-Bukhārī and Muslim).
وعن أنسٍ - ﵁: أنَّ رسول الله - ﷺ - دَخَلَ عَلَى ابْنِهِ إبْرَاهيمَ - ﵁ - وَهُوَ يَجُودُ بِنَفسِهِ، فَجَعَلَتْ عَيْنَا رسولِ الله - ﷺ - تَذْرِفَان. فَقَالَ لَهُ عبدُ الرحمانِ بن عَوف: وأنت يَا رسولَ الله؟! فَقَالَ: «يَا ابْنَ عَوْفٍ إنَّهَا رَحْمَةٌ» ثُمَّ أتْبَعَهَا بأُخْرَى، فَقَالَ: «إنَّ العَيْنَ تَدْمَعُ والقَلب يَحْزنُ، وَلاَ نَقُولُ إِلاَّ مَا يُرْضِي رَبَّنَا، وَإنَّا لِفِرَاقِكَ يَا إبرَاهِيمُ لَمَحزُونُونَ». رواه البخاري، وروى مسلم بعضه. والأحاديث في الباب كثيرة في الصحيح مشهورة، والله أعلم.
And from Anas (may Allah be pleased with him): that the Messenger of Allah (peace and blessings be upon him) came in upon his son Ibrāhīm (may Allah be pleased with him) while he was breathing his last, and the eyes of the Messenger of Allah (peace and blessings be upon him) began to shed tears. ʿAbd al-Raḥmān ibn ʿAwf said to him: 'Even you, O Messenger of Allah?!' He said: 'O son of ʿAwf, it is a mercy.' Then he followed it with another statement and said: 'Indeed the eye sheds tears and the heart grieves, but we say only what pleases our Lord; and indeed we are grieved at parting from you, O Ibrāhīm.' Al-Bukhārī narrated it, and Muslim narrated part of it. The hadiths on this chapter are many, well known in the Ṣaḥīḥ; and Allah knows best.