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NovusFidem
Guest
Even as a Catholic, we sometimes struggle with Mary veneration (hyperdulia). Mostly, this struggle happens because we, as many Protestants, fail to see the difference between adoration and veneration.***Turn, then, most gracious Advocate, thine eyes of mercy toward us; ***and after this our exile show unto us the blessed fruit of thy womb, Jesus; O clement, O loving, O sweet Virgin Mary.
To me, that sounds like Mary is being given divine characteristics instead of being the godly young girl that she was who took a great risk to her own life to say “Yes” to God and give birth to out Lord and Savior and to love Him and raise Him and to be there for Him and not abandon Him at His crucifixion.
But, just to clear some things. Just like the names say - Advocate, Mediatrix, etc - it should be clear as to the role of Mary.
Let’s pretend life is a courtroom. Think of Jesus as the Judge - He is the one and only to truly give us absolution, to declare us “not guilty”. He knows what we did, as He is a GREAT Judge (being omniscient and all that), He has all the facts, the clues and evidences of our crimes. He is very kind, but also very just/righteous.
We, as the defendant, can plead our own case (ask forgiveness, do good works, pray for ourselves and others), but after that (when we die) our chance of speaking is over. :imsorry:
Other people (alive) and the Saints (alive in Heaven) are witnesses of our life. Their prayer for us would equal to their testimony - they “help our case”.

Mary is our lawyer (Advocate, Mediator between us and the Judge). She is the one to plead our case after all is said and done. She does this because she is very kind.
Like in real life, think that there is a lot that can still be said. Like “sure, he killed someone and has to pay; but don’t you think that death penalty is too much? Can’t we work out some life sentence with hard labor” and such. Jesus has the facts, and He is just. We would think that nothing can change His judgement (as it is perfect), but then…
Our Lawyer is His Mother
I speak all this in jest, but the idea is basically this. Just like Mary, with only a simple request, somehow ‘convinced’ Jesus to perform His first miracle in the marriage at Cana, even though His time for that had not yet come:
What couldn’t she do for us as our Advocate/the Mediator between us and the Judge?“3. When the wine was gone, Jesus’ mother said to him, ‘They have no more wine’. 4. ‘Woman, why do you involve me?’ Jesus replied. ‘My hour has not yet come.’” - John 2:3-4
Our devotion to Mary should be seen more in a sense of humility. We are not worthy of our Lord, so we appeal to the intercession of Mary. While our Lord does invite us to talk to Him directly (and we do), we also talk to Him indirectly. The Hail, Holy Queen prayer that you mentioned, contains this part (that I particularly love):
"-. Pray for us, O Holy Mother of God.
No one goes to Mary, if not to request of her an “audience” with her Son. As the part of the Hail you posted does say: “show unto us the blessed fruit of thy womb, Jesus”.-. That we may be made worthy of the promises of Christ."
When we go for Mary, we go with the intent to meet her Son through her. And this is not a Godly power, by any means. Many of us “meet” Jesus through someone’s homily, preaching or testimony. Many of us first “met” Jesus because someone else told us about Him. Isn’t that why we must go everywhere to evangelize?
Tl:dr: So, yeah. Mary, to us, is just like any other person alive or Saint, with the additional that she IS Theotokos - Mother of God. If there is one person’s judgement Jesus would consider over everyone else’s, it is His own Mother. Our Veneration (dulia) to her and the Saints is nothing more than the fact that we consider both of them alive and, thus, they can pray for us. The special veneration (hyperdulia) reserved for Mary over the Saints (but still under the cult and Adoration - cultus latria - reserved for God alone), comes from the fact that she is “more special” than all the others
If people can pray for you, so can the Saints. If the Saints can pray for you, so can Mary. And, out of all of them, whose prayers do you think would be most effective beside your own?
Hope I helped some! I used to have trouble with all the images and Mary attention, but it makes sense in context