Dear Mark,

I did some digging on the Internet in an attempt to find an answer, but nothing really jumped out as satisfactory.  It seems nobody really knows for sure WHY this started, however the Middle Ages was frequently mentioned as a start time.  It seems that the practice was officially limited to two weeks during the 17th century, and then following Vatican II it is officially recommended to begin after Holy Thursday although the two week period is still permitted (Paschale Solemnitatis)

Back to your question WHY, the best reason I could find is because of the Gospel reading of that Sunday, which was the passion according to John.  (remember this is an old rite)  John 8:59 reads "They took up stones therefore to cast at him. But Jesus hid himself, and went out of the temple".  This is the explanation that is offered in the Catholic Encyclopedia, in fact the article mentions that the cross was covered at the exact moment those words were pronounced during the reading.  (article: "Passiontide")

Another reason I read was more practical... in order to be unveiled on good Friday, the crucifix must first be veiled.

When I first read your question I was tempted to answer with "progressive solemnity", the idea that more solemn liturgical celebrations and feasts such as Easter and Christmas are filled with more "stuff", by that I mean fancier louder music, more flowers, more bells, incense etc.. and that simpler occaisions and seasons such as Advent and Lent are celebrated more quietly, with no flowers and little or no music.

Historically speaking though I wasn't able to find any evidence that this is the reason why crucifixes and statues were veiled.

Mr. Slavek