To understand the biblical roots of our beliefs, you first have to be familiar with the concept of Typology - Typology in the Bible is a study comparing elements of the Old Testament to corresponding elements of the New Testament, finding symbolic, textual and contextual details in the Old Testament present in the New Testament, and further finding these same elements in the New Testament fulfilling or completing the Old Testament. In typology, the New Testament fulfilment is always greater than the Old Testament prefiguring symbol or event.
This is not a new concept, as St. Paul directly refers to Typology by name in Romans 5:14. So the study of typology is Biblical itself.
The background for our Old Testament context, in the early Middle Eastern kingdoms, especially the Davidic kingdoms of Israel the queen wasn't the king's wife. Kings had multiple wives. Each of the wives was interested in her own advancement and position and that of their own sons. The palace was rife with drama as the wives competed against each other to try to ensure that their own son would be the heir to the throne. When a man became King in this atmosphere, he couldn't trust his wives with his best interest. In these cases, the only woman he could truly trust was his own mother. His mother then became his most trusted ally, confidante and advisor. Therefore, it was his mother that acted as queen. We see this in the Old Testament. Bathsheba is one of the wives of King David. Solomon is the son of Bathsheba and David. When their son Solomon becomes king, Solomon sets up a throne for his mother, making Bathsheba queen. Further, in 1 Kings 2: 13-21 a favor is asked through Bathsheba. Solomon tells her that he cannot refuse any request.
In comparison, in the New Testament, at the Wedding at Cana, the servants do not go to Jesus, they go to Mary. When Mary brings the request to Jesus, while Jesus protests, not only can he not refuse her request, but she is completely confident that he will grant the request.
No one doubts that Jesus is our King. If he is our King, in the line of David, who would then be our Queen? His mother, of course. This well-established Old Testament arrangement would also be true in the New Testament. But the kingship of Jesus is greater than that of David or Solomon; therefore the queenship of Mary must also be greater. If there is any doubt, this is further confirmed in Revelation 12:1 when we see the Woman crowned. Biblical scholars agree that the woman referred to in Revelation 12 is Mary.
Rev 12:1 A great sign appeared in the sky, a woman clothed with the sun, with the moon under her feet, and on her head a crown of twelve stars.
As you can see, contrary to being a "man-made tradition;" this belief is strongly rooted in scripture.