Why do women no longer have to have their head covered while at mass?  And why do some still do it?

There has long been a practice of women covering their heads in public, and especially in holy places, across religious traditions.  Paul makes note of it in 1 Cor 11:4-16.  Drawing upon this, as well as tradition and local custom, as in the Middle East, the 1917 Code of Canon Law originally required women to cover their heads in church (#1262).

Especially after Vatican II, the practice of wearing veils has largely faded away among Catholics in the West; non-Western Catholics and those who prefer a traditionalist or Tridentine observance of the faith here may still wear them more regularly.  Some say this veil was a casualty of feminist resistance as well as the decline of hats as part of fashion and social custom more generally.  But the 1983 Code of Canon Law omitted any ruling on veiling, perhaps as an accommodation to Vatican II’s attempts to modernize the Church. There is some dispute on whether this omission cancels out the 1917 canon on this matter.