What follows is a selection of quotes from early fathers on veiling and women's attire. I'll let them speak for themselves.
But we admonish you, too, women of the second (degree of) modesty, who have fallen into wedlock, not to outgrow so far the discipline of the veil, not even in a moment of an hour, as, because you cannot refuse it, to take some other means to nullify it, by going neither covered nor bare.
(...) Arabia's heathen females will be your judges, who cover not only the head, but the face also, so entirely, that they are content, with one eye free, to enjoy rather half the light than to prostitute the entire face.
It is incumbent, then, at all times and in every place, to walk mindful of the law, prepared and equipped in readiness to meet every mention of God; who, if He be in the heart, will be recognised as well in the head of females. To such as read these (exhortations) with good will, to such as prefer Utility to Custom, may peace and grace from our Lord Jesus Christ redound
- Tertullian, "On the Veiling of Virgins." approx 200 AD
"Let the woman observe this, further. Let her be entirely covered, unless she happens to be at home. For that style of dress is grave, and protects from being gazed at. And she will never fall, who puts before her eyes modesty, and her shawl; nor will she invite another to fall into sin by uncovering her face. For this is the wish of the Word, since it is becoming for her to pray veiled." [Clement, The Instructor 3.12]
Clement of Alexandria, Egypt, approx 190 AD
"And let all the women have their heads covered with an opaque cloth, not with a veil of thin linen, for this is not a true covering."
-- Hippolytus (200 AD), Apostolic Tradition
“Woman, because she was created by being drawn from man’s side, is constantly trying to return to him. She desires the original unity of one flesh and one bone. The desire for unity between man and woman is a mirror of the relationship between Christ and the soul. As woman longs for union with man in human relationships, she is also drawn to unity with God. He calls her to become one with Him: to come under His side and become flesh of His flesh and bone of His bone. This occurs during reception of the Eucharist. The covering of the head with a veil symbolizes the reality of woman sheltered in the side of her Source and becoming one with Him. She becomes covered and hidden in her Divine Spouse.”
~ St. John Chrysostom, Father and Doctor of the Church