About the proof of a practice of cutting and then offering the hair, archaeology appears as the most numerous and increasing as history advances. 
Anyway, the remains from the Late Period come from a unique necropolis with ten tombs having hair offerings. But, again the New Kingdom has more indices of it, with many scenes where mourning women appear with short hair.
The two Drty (two kites), offering nw vases to the four pools. Relief from the tomb of Pahery in el-Kab. XVIII Dynasty. Photo: http://www.osirisnet.net
Does it mean that this practice becomes popular as time goes by? Or again does it come about by chance? If the Coffin Texts of the Middle Kingdom give us indices of cutting the mourning women’s hair we have to suppose that this was not a new practice included suddenly in the sacred texts.
HAIR AND DEATH IN ANCIENT EGYPT 