Vinny, obviously, there's nothing you can do to reduce the weight if all of the tools are packed together. I use a square-shaped bag I bought at Home Depot. It's almost perfect.
It has 3 open-top compartments; the two side ones have separators, smaller pockets, and elastic bands. I use these for folding rulers, stud-finders, chisels, drywall saw, coax and UTP tools, etc.
There are multiple outside pockets for screwdrivers, pliers, etc., and a velcro-flapped pouch, a tape-holding strap (which I have 4 rolls on).
The neatest feature (to me) is the compartment underneath that holds a multi-compartment plastic box, which I use for wirenuts, staples, etc.
It sounds like you could use two, both for balance when you need everything, and for reducing weight when you can separate your toold into two basic types of work.
I don't remember the name of the bag, but it will either be in the electrical department, or with the toolboxes. It comes with both a short hand strap and a shoulder strap. It's a soft-sided bag. It's stiff enough to hold its shape, but it's made of a very durable material.
Larry
www.fineelectricco.com