If you have ever paid close attention to the Church's Marian hymns and prayers, there exists a particular pattern to each of them.
The Catechism of the Catholic Church separates the pattern into two distinct "movements":
Beginning with Mary's unique cooperation with the working of the Holy Spirit, the Churches developed their prayer to the holy Mother of God, centering it on the person of Christ manifested in his mysteries. In countless hymns and antiphons expressing this prayer, two movements usually alternate with one another.
Magnifying the Lord
[T]he first "magnifies" the Lord for the "great things" he did for his lowly servant and through her for all human beings.
The Magnificat as well as the Hail Mary both contain this first movement.
Intercessory prayer
[T]he second entrusts the supplications and praises of the children of God to the Mother of Jesus, because she now knows the humanity which, in her, the Son of God espoused.
Again, the Hail Mary is a perfect example of this second movement, ending the prayer with, "Pray for us sinners.."
While these two movements are not in every single Marian prayer, this pattern is repeated over and over again in many of the Church's most popular prayers.