Medieval women actually had much more rights and autonomy in the Middle Ages than women did either in ancient Rome or in the modern period (before around the 1920s). They certainly did not have what we would now call "equal rights," but then neither did most men. Some careers, like the priesthood, were closed to women, but this did not keep them from having a great deal of influence.
Christianity stressed that women and men were equal in the eyes of God, which put them well ahead of the women in ancient pagan Rome.
As I noted before in a post on medieval marriage, the heart of a valid marriage was the consent of the two parties, which meant that a woman could not be married against her will, any more than could a man. In practice of course young women would be heavily pressured by their relatives into choosing whom the relatives thought an appropriate spouse, but then young men experienced similar pressure.
Although women could not be priests, they could become nuns. In the early Middle Ages, it was fairly common to have a double monastery, one house for men and another for women, with a single head--and the head would be an abbess, a woman, because it was considered wrong for women to be under a male abbot. Even abbesses who only ruled over women in their nunneries could and did influence men. Hildegard of Bingen, twelfth-century abbess of a German nunnery, who had mystic visions greatly admired by men, wrote to bishops and even to popes to straighten them out on key details.
(Hildegard also wrote a lot of really lovely music for her nuns, which is still being performed and recorded. She has recently been adopted by New Age folks, which Hildegard, a traditionalist Christian, would have found appalling.)
Women were as likely as men to know how to read and write, and aristocratic women taught their children, both boys and girls, their first lessons. (Literacy was low by our standards, but it was not determined by sex.)
It was appreciated that women were weaker physically than men, but this was taken as a reason to see them as spiritually stronger--they had more to overcome (Peter Abelard especially made this point). If some argued that sin first came into the world via a woman, Eve, then others argued equally vehemently that salvation came into the world via Mary, because Jesus would not have been able to save humans if he had not had human flesh, which he got from her--and, in addition, women were the first to see the risen Christ.
In nineteenth-century England, married women's property became their husband's property, but this was not true in the Middle Ages. If a medieval woman wanted to sell or give away her own property, she was free to do so, although she would generally have her husband formally agree. He on the other hand could not give away or sell her property and would need her consent to do anything with his own.
Interestingly, medieval spouses did not inherit from each other. Among the aristocracy, widows generally had a right to a third of their late husband's property for their lifetime, but they could not sell it or give it away, because it wasn't theirs. Property instead was inherited by the children of a couple, or in the absence of children, by the relatives of the late couple, her property going to her relatives, his to his. Widows could and did become regents for their minor children, effectively ruling great estates, even duchies, even if in the name of an infant son (see more here on regency).
In many occupations, like farming, husbands and wives worked side by side. In the guilds, women could become masters, even though most of the masters were men--only the guilds of professors and merchants were closed to women, and on the other hand men couldn't join the ribbon-makers' guild. Women ran the castles, as everyone knew, including the titular lords of the castles.
Click here to see more on medieval women.