“To dedicate Saturday in honor of Mary is an ancient custom. It is based on a legendary account that Jesus appeared to Mary on the Saturday, the day after His death. He did so to reward her for her steadfast faith in His divinity, which did not waver under the Cross. Another strain of devotional thought explains that Divine Wisdom, becoming flesh of the Virgin Mary, rested (Saturday=Sabbath=day of rest) in Mary as on a bed.
‘One of the oldest customs traced to honoring Mary on Saturday in the Church of Rome took place on the Saturday before “Whitsunday” [White Sunday]. The newly-baptized members of the Church were led from St. John’s baptistry of the Lateran to Mary’s great shrine on the Esquilin, St. Mary Major [built under Pope Liberius 352-66]. St. John of Damascus’ († 754) writings testify to the celebration of Saturdays dedicated to Mary in the Church of the East. The liturgical books of the ninth and tenth centuries contain Masses in honor of Mary on Saturday.”
Excerpt taken from: http://campus.udayton.edu/mary/resources/firstsaturday.html You can go to this University of Dayton website for more information on this and other Marion days.