The scriptural origin of the first part of the Hail Mary is in the Gospel of St. Luke. It is a comination of the first words of Gabriel to Mary (Luke 1:28) and the greeting of Elizabeth to her cousin Mary (Luke 1: 42) Full of grace indicates that Mary is highly favored. "The Lord is with you is affirmation.
"Blessed are you among women" prefigure what Elizabeth with say to Mary in Luke 1:42.
Blessed is the fruit of your womb. (Deuteronomy 28:4)
The second part of the Hail Mary is not biblical. It was added by the Church in supplication to the Mother of God, asking for her intercessory prayers for us sinners, and the necessary grace for our salvation now, and at the hour of our death.
The only belief of the Holy Roman Catholic Church about Mary, not specifically mentioned, is her perpetual virginity.
Thanks to Beads and Prayers: The Rosary in History & Devotion, by John D. Miller, pp. 31-37.