most PC case weighs so your request is hardly possible. to
mostpc builders who are in to games, their concern is never the
weight. god knows shit happens but for them they are concerned
about compatibility issues and most of all - the performance.
if u want a lighter PC gaming rig get an alluminium case as
compared to steel cases they are lighter.
my suggestion is if you need to bring your whole PC down to a tech
guy to look inot, just dismantle and remove all the cards and hard
disks and power-on card ( with push button) in the case and bring
it over to the tech. set up there (withoout the case is possible)
and let the guy work on the system for you. 
ok serious, some gaming cases come with a carrying handle at the
top so its more convenient to be moved around. Some Antec LanBoy
cases have strap-ons that allows the case to be slung over like a
haversack or bag, or hand-carried like a suitcase. you should check
out such cases.
back to the wieght there is nothing much we can say 'cept that the
total weight of the hdds, boards and cards and Psu weighs just so
and the better part of the difference lies on the case itself.