I wrote a big post yesterday but I guess I forgot to submit it :`
Anywhoo... we do chamber bodies that do not have back laminates, and we hog is out a bit more than the illustration above. To make it lightest weight though, use a top and back and have the construction fully hollow core. Skip the tummy and elbow shaping and we can make it more hollow.
Other ways to lighten things up: make the neck width as small as you can stand it. Really, I mean, stress yourself even if only slightly, and it will pay off big time in the weight. The neck is the heaviest thing (it's not hollow and only gets transected by the pickups and bridgeblock, which are both heavy). The smaller you get the neck, the less fatiguing the bass will be to play both for the fingers and the back. 32 scale will help too.
Further on the neck, if you don't mind the warmer sound, use Mahogany for the primary neck wood.
To understand how the density of the wood affects the overall weight, consider the Essence 4-string bass. A typical one weighs in at about 8.5 pounds. Mine is made from Cherry and Kingwood with a Maple and Purpleheart neck and it weighs 10.75 pounds. We made an lightweight Essence with a Mahogany, Walnut and Birch neck and a Mahogany Zebrawood body that weighed in at about 6.5 pounds.
Other little things you can do is to swap out for Hipshot Ultralight tuners. Have a wooden bridgeblock made so you can swap it out and see if you need the extra mass for sustain (or opt out of the block entirely). Use plastic or wooden backplates. Have the shim style tailpiece. Every ounce here and there will add up.
And Gregory, you're right about the body shape sizing. Standard Omega is large, Anniversary Omega is medium and the 3/4 is the smallest. Of course, you'll have to consider that upper horn length for the balance of the whole thing - no point in making it light weight then having it neck heavy.
Lightest weight top wood is Curly Redwood - but note that like most lower density woods, it will keep the bass less bright that using higher density woods. Not so noticeable with a Maple neck, but remember every specification has its tradeoffs, and you have to prioritize what attributes are most important to you.