Do Catholics worship Mary?

No. Catholics do not worship Mary. Worship (latria) is given to God alone. Catholics venerate Mary (hyperdulia) as the Mother of God and a preeminent saint, asking her intercession just as one might ask a fellow Christian to pray on their behalf.

Distinguishing Devotion from Worship

In short, to venerate Mary is to honor the masterwork of God's grace. To worship her would be a grave sin. Catholics do the former and categorically reject the latter.