Sometimes even us Catholics have hard time giving Mary praise because we think it might take away from the praise due to God. It may seem like a valid fear, but one needs to look more carefully at the difference between worship and praise. God commands that we never worship anything or anyone but God, so we never worship Mary. She is not a goddess and Catholics never make that claim. We always understand that she is only a mortal, just like you and me, but unlike any other mortal, she has been given a title that no other before or after her can ever claim. She is the Mother of God. God saw her humility and gave her the honor of bearing his Son. But it doesn't stop there. At the foot of the cross, he also gave her the honor of Mother of all humanity when he said to John, "Woman, behold your son." Then when she was assumed into heaven, he gave even more honor. He made herof all graces, and crowned her Queen of Heaven and Earth. Because of all these honors God has given her, it is only fitting for us to praise her and honor her the same as Our Lord has done.
We should never fear giving her too much honor and praise. She keeps nothing for herself and gives all the glory to her Son. In fact, she gives more glory to her son than we can give to him. Since our prayers are filled with our many vices, sins and distractions, they are less than perfect. But Mary's prayers are always perfect because she is full of grace. If we give our prayer to Mary, and ask her to give them to her son, we can be sure that our imperfect prayers are made more perfect and pleasing to God than we could ever do on our own.
"Mary, the exalted daughter of , helps all her children wherever they may be and whatever their condition, to find Christ the path to the Father's house."
--Pope John Paul II ( Mater, n. 47) You can find the entire encyclical here (which has just been added to my reading list.)