You're kidding right? If you want to shave weight, remove the rear brake.
Also learn to pedal standing up, remove the seat and seat post all together along with the handlebar and stem, just grip the front brake lever in your hand and steer the nub on the headset with the other.
You can shave a couple hundred grams if you remove the tires and tube and ride on the rims. Find a smooth road and take out every other spoke, just really really tension the remaining ones. If you do this, you can also remove the pump and patch kit. Remove the front and derailler also along with two rings from the front and all but one gear from the rear cassette.
Use a chaintool to break all the links in your chain, use every other plate only. Remove the pedals and replace them with a thin rod. Uh.. I think you'll be good there.
On my bike, the front brake's worn down to half, the rear brake's almost untouched. In an emergency, I grab both but usually the front works a lot better, the rear just locks up and I go all wiggly and slide.