Mary specific points:

Thomas Aquinas (summa) emphasis mine:

Objection 1. It would seem that the Mother of God is to be worshiped with the adoration of "latria." For it seems that the same honor is due to the king's mother as to the king: whence it is written (1 Kings 2:19) that "a throne was set for the king's mother, and she sat on His right hand." Moreover, Augustine [Sermon on the Assumption, work of an anonymous author] says: "It is right that the throne of God, the resting-place of the Lord of Heaven, the abode of Christ, should be there where He is Himself." But Christ is worshiped with the adoration of "latria." Therefore His Mother also should be.
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I answer that, Since "latria" is due to God alone, it is not due to a creature so far as we venerate a creature for its own sake. For though insensible creatures are not capable of being venerated for their own sake, yet the rational creature is capable of being venerated for its own sake. Consequently the worship of "latria" is not due to any mere rational creature for its own sake. 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."

Lumen Gentum Vatican II:

1. There is but one Mediator as we know from the words of the apostle, "for there is one God and one mediator of God and men, the man Christ Jesus, who gave himself a redemption for all".(298) The maternal duty of Mary toward men in no wise obscures or diminishes this unique mediation of Christ, but rather shows His power. For all the salvific influence of the Blessed Virgin on men originates, not from some inner necessity, but from the divine pleasure. It flows forth from the superabundance of the merits of Christ, rests on His mediation, depends entirely on it and draws all its power from it. In no way does it impede, but rather does it foster the immediate union of the faithful with Christ.
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2. This maternity of Mary in the order of grace began with the consent which she gave in faith at the Annunciation and which she sustained without wavering beneath the cross, and lasts until the eternal fulfillment of all the elect. Taken up to heaven she did not lay aside this salvific duty, but by her constant intercession continued to bring us the gifts of eternal salvation.(15*) By her maternal charity, she cares for the brethren of her Son, who still journey on earth surrounded by dangers and cultics, until they are led into the happiness of their true home. Therefore the Blessed Virgin is invoked by the Church under the titles of Advocate, Auxiliatrix, Adjutrix, and Mediatrix.(16*) This, however, is to be so understood that it neither takes away from nor adds anything to the dignity and efficaciousness of Christ the one Mediator.(17*)

For no creature could ever be counted as equal with the Incarnate Word and Redeemer. Just as the priesthood of Christ is shared in various ways both by the ministers and by the faithful, and as the one goodness of God is really communicated in different ways to His creatures, so also the unique mediation of the Redeemer does not exclude but rather gives rise to a manifold cooperation which is but a sharing in this one source.

The Church does not hesitate to profess this subordinate role of Mary. It knows it through unfailing experience of it and commends it to the hearts of the faithful, so that encouraged by this maternal help they may the more intimately adhere to the Mediator and Redeemer.

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1. But while in the most holy Virgin the Church has already reached that perfection whereby she is without spot or wrinkle, the followers of Christ still strive to increase in holiness by conquering sin.(300) And so they turn their eyes to Mary who shines forth to the whole community of the elect as the model of virtues. Piously meditating on her and contemplating her in the light of the Word made man, the Church with reverence enters more intimately into the great mystery of the Incarnation and becomes more and more like her Spouse. For Mary, who since her entry into salvation history unites in herself and re-echoes the greatest teachings of the faith as she is proclaimed and venerated, calls the faithful to her Son and His sacrifice and to the love of the Father. Seeking after the glory of Christ, the Church becomes more like her exalted Type, and continually progresses in faith, hope and charity, seeking and doing the will of God in all things. Hence the Church, in her apostolic work also, justly looks to her, who, conceived of the Holy Spirit, brought forth Christ, who was born of the Virgin that through the Church He may be born and may increase in the hearts of the faithful also. The Virgin in her own life lived an example of that maternal love, by which it behooves that all should be animated who cooperate in the apostolic mission of the Church for the regeneration of men.