Why are/were Catholic women asked to cover their heads in the presence of the Blessed Sacrament and at Mass?
While the 1917 code of canon law required women to cover their heads at church, the 1983 code of canon law does not contain that provision and thus it is abrogated (canon 61). However if someone attends the Extraordinary Form of the Mass then she should follow the 1962 rules and wear a head covering.
The origins of head coverings for women in church are from 1 Cor. 11:3-16. It is an ancient form of modesty and respect which the Church continued on until modern times.
As the CDF’s Inter Insigniores noted:
But it must be noted that these ordinances, probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance, such as the obligation imposed upon women to wear a veil on their head (1 Cor 11:2-16); such requirements no longer have a normative value.