Depending on your class regs, losing weight can be pretty easy.
Cage material can make a big difference (cromol versus cold drawn)
Pulling up all the sound deadening from the thing helps, scraping all the stone guard from under the car too.
Then you look at other things like bar reos, non-structural supports etc etc, start with a set of holesaws and just go to town.
Its a bit easier/lenient with the speedway regs, but same thing applies to you guys, anything non essential goes in the bin or gets a hole drilled in it.
What are the regulations on door internals? Can you fit fixed lexan windows to the rear?
that sort of thinking shaves a heap of weight.