His own tears, and the actual limit
These two reports must always be read together, because read apart the second one is used to silence people.
The first is the death of the Prophet's infant son Ibrahim. He held him and kissed him, and as the child was dying his eyes shed tears. One of the Companions said, even you are weeping. He said, this is mercy. Then he wept more and said that the eyes shed tears and the heart grieves, and we say nothing except what pleases our Lord, and that they were grieved by the separation.
The second is the report that the one who slaps his cheeks, tears his clothes and follows the ways of ignorance is not one of us. That is the limit, and notice precisely where it falls. It is on ritualised, destructive lamentation, striking the face, tearing clothing. It is not on tears, because the first report is tears at a graveside from the very person delivering the second.
Qur’an and Sunnah
Narrated Anas bin Malik:We went with Allah's Messenger (ﷺ) to the blacksmith Abu Saif, and he was the husband of the wet-nurse of Ibrahim (the son of the Prophet). Allah's Messenger (ﷺ) took Ibrahim and kissed him and smelled him and later we entered Abu Saif's house and at that time Ibrahim was in his last breaths, and the eyes of Allah's Messenger (ﷺ) started shedding tears. `Abdur Rahman bin `Auf said, "O Allah's Apostle, even you are weeping!" He said, "O Ibn `Auf, this is mercy." Then he wept more and said, "The eyes are shedding tears and the heart is grieved, and we will not say except what pleases our Lord, O Ibrahim ! Indeed we are grieved by your separation
Sahih al-Bukhari 1303graded sound, sahihaynfull report
Narrated `Abdullah:the Prophet (ﷺ) said, "He who slaps his cheeks, tears his clothes and follows the ways and traditions of the Days of Ignorance is not one of us
Sahih al-Bukhari 1294graded sound, sahihaynfull report