This question comes in many forms, but generally expresses a belief that Catholics are worshipping Mary. Catholics have a very close relationship with the Blessed Virgin Mary, and from the outside this appears to be worship. However, Catholic teaching forbids worship of anyone or anything other than God. Only God is to be worshipped. There are no exceptions, no debate, it's not even a gray area. Mary, like us, is a creature. No creation, no creature is to be worshipped.
We do honor Mary. We honor her because God honored her. God honored Mary by making her His Mother. Further, Jesus honored her because she was His Mother. Jesus would have perfectly followed the commandment to honor your father and your mother. So when we honor Mary, we are emulating Jesus. We could never honor her as much as Jesus, in his perfection, honored her.
Keep in mind also we are following the Bible. In Luke 1:48 Mary herself recognizes that God has honored her and that all generations will call her Blessed. So if you are not recognizing her Blessed status, are you following the Bible?
And we recognize her as queen. In Revelation 12:1 we see her crowned with a crown of 12 stars. Notice the correlation to the 12 Apostles, who were to sit on 12 thrones to sit in judgment of the 12 tribes in Matt 19:28. But even more important, she was the queen mother. In the Middle Eastern kingdoms of the time, and specifically the Davidic kingdoms of ancient Israel, the queen wasn't the wife of the king, but rather the queen was his mother. A king had many wives. And in the politics of the royal family, each wife would focus on gaining power and position for her own son. The only woman a king could trust was his own mother. It was his mother that he would turn to for advice. And it was his own mother that would sit beside a king and help him rule. In 1 Kings 2:19, King Solomon bowed down before his mother, and then provided a throne for her at his right-hand side. And in Verse 20, Bathsheba makes a request to her son, and he says he cannot refuse her. Notice how this parallels with the wedding at Cana in John 2 when the mother of Jesus prompts him to begin his ministry. She makes a request, knowing he will not refuse. We all agree that Jesus is King; that would make his mother the queen. The wedding at Cana sets it up, and Revelation confirms it.
It is important to note that while there are teachings regarding our Blessed Mother that are firm matters of faith, it is not required of Catholics to pray to our Blessed Mother, or any of the saints. Not specifically, anyway. Our unity with the saints is told in the book of Revelation. The unity of the Body of Christ includes all Christians, both now and those that came before us. It is our privilege; we have been given the gift of membership in the Body of Christ. And as St. Paul tells us in 1 Cor 12:21, we need each other, the entire body of Christians. And we express our bond by caring for each other, and by praying for each other. And just as I might ask you to pray for me, I can also ask for the saints in heaven to pray for me. As James says in James 5:16, the prayers of a righteous man are powerful, and pray for one another. Who could be more righteous than someone already in heaven?
The Marian traditions that we follow are so rich, beautiful and full. But they all remind us that our Blessed Mother has a role in our salvation. It is her job, now as it was 2,000 years ago, to bring Jesus to us. Books have been written on the topic, and there is so much history on the subject. It's a topic that could be studied for years, and still there would be more to learn. But remember, all of this is for our benefit, to help bring us closer to Jesus, no more, and certainly no less.