I guess because people think it will bring blessing to the marriage, like starting off the marriage (from the first steps when she is leaving with the groom) under the blessing and protection of the Quran..something like this
I dont like this rasm at all. Thank God no one tried to do it on my wedding. If you want the blessing and protection of Allah in your marriage and in your life then why not actually open the book, read it, and act upon it, instead of wrapping it up in a shiny cloth and holding it over your head and meanwhile doing everything else at your wedding that goes against the teachings of the Quran. It doesnt make much sense...at least not to me
I found out that this was an old hindu tradition, they would hold the gita or holy book over the head of the bride as a form of blessing. Muslims took it up over the years. Practically all the girls on my moms side (in Pakistan) have had it done to them. No one is going to do it on my wedding as my Dad's side don't have this rasam.
I heard that Mehndi was a hindu tradition, but actually found out it's an old mughal tradition for muslim brides. Note that Turkey, Morocco, Iran, Bangladesh amongst other have a mehndi tradition too.