Why did Mary ask Jesus to make wine at the Wedding at Cana The Wedding at Cana is the only instance AFAIK where Mary asks Jesus to perform a miracle. 

Is there any indication or insight as to why she did so ? Was the family very close to her/them ?

Or was it simply the time for Jesus to perform a public miracle and it came about in this manner?
Catholics love Mary, as you may know. And this particular detail of the Wedding of Cana reaffirms the Catholic devotion to Mary as an intercessor.


  The Gospel reveals to us how Mary prays and intercedes in faith. At
  Cana, the mother of Jesus asks her son for the needs of a wedding
  feast; this is the sign of another feast—that of the wedding of the
  Lamb where he gives his body and blood at the request of the Church,
  his Bride. It is at the hour of the New Covenant, at the foot of the
  cross, that Mary is heard as the Woman, the new Eve, the true “Mother
  of all the living.” (Catechism of the Catholic Church)


As Christ is an embodiment of something, that of God's self-proclamation and self-incarnation of His own saving power, Mary is also an embodiment of something, namely the human "yes" to God's will. As such, she is the primary intercessor of the Church to Christ.

Extrapolating a little: By her acceptance to receive God in her flesh, we acknowledge her mission as an intercessor (Queen among many) from God to man. And by her request at the wedding of Cana (which Jesus was undoubtedly waiting for), we acknowledge the validity of her mission as an intercessor from man to God.