“You shall worship the Lord your God and him only shall you serve.”
Short answer
The Church gives adoration to God alone. Mary is honored because of what God did in her, and every honor paid to her is meant to end in her Son. The Fathers and the councils drew that line in so many words.
Drafted from primary sources. The project folder holds only two short quotations on Mary so far.
16 quotations in date order
“Hail, full of grace, the Lord is with you! … Blessed are you among women, and blessed is the fruit of your womb! And why is this granted me, that the mother of my Lord should come to me? … For behold, henceforth all generations will call me blessed.”
“Do whatever he tells you.”
“For Eve, who was a virgin and undefiled, having conceived the word of the serpent, brought forth disobedience and death. But the Virgin Mary received faith and joy, when the angel Gabriel announced the good tidings to her.”
“And thus also it was that the knot of Eve's disobedience was loosed by the obedience of Mary. For what the virgin Eve had bound fast through unbelief, this did the virgin Mary set free through faith.”
“We fly to thy protection, O holy Mother of God. Despise not our petitions in our necessities, but deliver us always from all dangers O glorious and blessed Virgin.”
“Mary was the temple of God, not the God of the temple. And therefore He alone is to be worshipped Who was working in His temple.”
“What is properly divine worship, which the Greeks call latria, and for which there is no word in Latin, both in doctrine and in practice, we give only to God. … Accordingly we never offer, or require any one to offer, sacrifice to a martyr, or to a holy soul, or to any angel.”
“So have they dared to call the holy virgin, mother of God, not as though the nature of the Word or his godhead received the origin of their being from the holy virgin, but because there was born from her his holy body rationally ensouled, with which the Word was hypostatically united and is said to have been begotten in the flesh.”
“Certainly this is not the full adoration (latria) in accordance with our faith, which is properly paid only to the divine nature.”
“Since, therefore, the Blessed Virgin is a mere rational creature, the worship of "latria" is not due to her, but only that of "dulia": but in a higher degree than to other creatures, inasmuch as she is the Mother of God. For this reason we say that not any kind of "dulia" is due to her, but "hyperdulia."”
“…it is good and useful suppliantly to invoke them, and to have recourse to their prayers, aid, and help for obtaining benefits from God, through His Son, Jesus Christ our Lord, who is our alone Redeemer and Saviour.”
“…the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin.”
“…the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory.”
“For no creature could ever be counted as equal with the Incarnate Word and Redeemer. … This cult, as it always existed, although it is altogether singular, differs essentially from the cult of adoration which is offered to the Incarnate Word, as well to the Father and the Holy Spirit, and it is most favorable to it.”
“The Church's devotion to the Blessed Virgin is intrinsic to Christian worship. … This very special devotion … differs essentially from the adoration which is given to the incarnate Word and equally to the Father and the Holy Spirit, and greatly fosters this adoration.”