The Prophet, sallallaahu ‘alayhi wa sallam, said to Abu Tharr: "O Abu Tharr, you are a weak man and it is a trust and it will be a cause of disgrace and remorse on the Day of Resurrection except for the one who takes it up with a full sense of responsibility and fulfills what is entrusted to him." What is meant by the saying of the Prophet, sallallaahu ‘alayhi wa sallam, to Abu Tharr: "You are a weak man."?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The meaning of the some of the words of the Hadeeth you are asking about was narrated on the authority of Abu Tharr who said, "O Messenger of Allaah! Why do you not appoint me as a governor?'' He patted me on the shoulder with his hand, and said: "O Abu Tharr, you are a weak man and it is a trust and it will be a cause of disgrace and remorse on the Day of Resurrection except for the one who fulfills its obligations and (properly) discharges the duties attendant thereon." [Muslim and Ahmad] Weakness in the Hadeeth means the inability to fulfill the duties of governorship. An-Nawawi said, "This Hadeeth is a great principle in keeping away from positions of authority, particularly for those who are too weak to carry out the duties of this position."

Allaah Knows best.