In general, according to the Holy Quran and the hadiths, all our deeds are offered to the Prophet (PBUH) and the Infallible (AS) Imams - especially the Imam of Time (AS) as the present Imam – and they not only observe the actions and deeds of the Muslims and become happy or sad, but also bear witness on the day of Resurrection based on what they have seen. But we couldn,t find a narration proving his crying due the sins that Muslims do.
It has been mentioned in the Holy Quran that says: and say do whatever you desire that Allah Almighty, his prophets and the believers will soon observe your deeds and you will soon be returned to the one who is all-knowing. Then you will be aware of what you used to do.it has been explicitly mention in a narration that the believers in this verse are the infallible Imams.
There is also a narration concerning the same issue that shows the depression and sadness of the Holy prophets peace be upon him and his progeny and the infallible Imams that the following narration is one of them.
Imam Sadiq (as) said: "Why are you saddening the messenger of Allah?" They said: "How do we do that?!" He replied, "Do you not know that your actions are both offered to him and seen by him, and if he sees sins in your actions, then he will be grieved and sad?" He then ordered: "Try to make the Prophet (pbuh) pleased and do not cause his displeasure.
source : erfan.ir