Why are Saturdays especially dedicated to the Virgin Mary?

In the Catholic Church, Saturdays are special days in the liturgy and are dedicated to the Virgin Mary. On most Saturdays throughout the year, priests may offer votive Masses in her honor, and in the Liturgy of the Hours, specific prayers and readings are dedicated to her.

But why Saturday rather than any other day? 

The tradition of honoring the Mother of God on Saturday is an ancient custom widely attributed to the Benedictine monk Alcuin (735-804), a close advisor to Charlemagne, who composed a votive office for each day of the week, and two offices especially for Saturday in honor of the Virgin Mary.

But this still does not tell us why Saturday and not another day. According to St. Thomas Aquinas, this choice has to do with the Resurrection of Jesus, which took place on a Sunday, and with the unshakeable faith of the Virgin on the previous day. (...)

Others have argued that since Sunday is dedicated to Jesus, it seemed logical to dedicate the previous day to his Mother.

Whatever its true origins, this Marian devotion on Saturday was confirmed during the private revelations of Our Lady of Fatima. Indeed, on December 10, 1925, the Virgin Mary appeared to Sister Lucia in the convent of Pontevedra, Spain. A few years earlier, Lucia had been one of the three seers of Our Lady's apparitions in the small Portuguese village. In this new private revelation that occurred eight years after the events of Fatima, Mary requested the establishment of the devotion of the first five consecutive Saturdays in reparation for the offenses done to her Immaculate Heart.

This apparition re-emphasized the existing link between Saturday and devotion to Our Lady, whose role has always been to draw the faithful to her Son Jesus. Saturday is a "day of preparation", and Mary is the one who prepares us to harvest the fruit of our labor on Sunday, the day of the Resurrection.

Adapted and translated from: https://fr.aleteia.org