If you are worried about weight, then look for the lightweight MDF (it costs more, but weighs 1/3 less) or use something other than MDF.
Routing out a huge area like that is silly in my opinion. It will take a while, make a huge mess and probably wont save you that much weight. If you route out half the thinckness down to 3/8" on both sides you might save yourself 10-15 pounds. Big deal.
*sarcasm on*
Why not cut a big ass window in the side of your cabinet, cover it with lexan and you can show off your case modding skilz. You could put lights and crud inside your case and people will ooh and ah.