Why do Shias cry so much during Muharrum?

Again, a rather simple answer - Shias are in mourning, crying is the natural response. People try to claim that somehow crying is wrong and un-Islamic but it has been encouraged by the Holy Prophet and is mentioned clearly in the Holy Quran.

"And when they listen to the revelation received by the Messenger, thou wilt see their eyes overflowing with tears, for they recognise the truth: they pray: "Our Lord! we believe; write us down among the witnesses." (Quran, Surah 5, Verse 83)

Shia Women Mourning during Muharrum

 

Surah Yusuf (no. 12) goes on to describe what happened to Prophet Yacub when he discovered that Prophet Yusuf had gone missing.

"And he turned away from them, and said: "How great is my grief for Joseph!" And his eyes became white with sorrow, and he fell into silent melancholy." (Quran, Surah 12, Verse 29)

Prophet Yacub cried so much his eyes went "white with sorrow." During the time of the Holy Prophet after the Battle of Uhud and the martydom of his uncle Hamzah, Tabari narrates in his book: "The Messenger of God passed by a settlement of the Ansar of the Banu Abdal al-Ashhal and Zafat and heard sounds of lamentation and women weeping. The Messenger of God’s eyes filled with tears and he wept, but then he said “Yet Hamzah has no women weeping for him”. When Saad bin Muadh and Usayd b. Hudayr came back to the settlement of the Banu Abdal al-Ashhal, they told the women to gird themselves up and go and weep for the Messenger of God’s uncle." (The History of the Prophets and Kings, Vol 7, pg 137) The Holy Prophet encouraged his followers to cry and mourn the loss of his uncle and yet we are not meant to cry when remembering the death of Imam Hussain (as).

This idea that it is somehow wrong to cry, to get emotional over such a loss is absurd. Hanafi scholar Sheikh Sulayman ibn Ibrahim Qandoozi sums it up best: "The grief of Imam Husayn (as) is the grief on which not only Humans, but even jinnat, Angels, animals, birds, the sky and trees, all lament. Thus it is written that the sky wept for forty days on (the martyrdom of) Imam Husayn (as)"