Since the rites of the Shrine are styled after Arabic themes and imagery, Shriners wear the Fez as a mark of their membership in the same way that a Master Mason wears the white lambskin.
The Fez reminds us of our Masonic apron when we wear it. … The fez makes us visible. It makes us memorable.
More information on Sizes can be found here: http://www.dturin.com/images/HatSizeGuide.pdf