The weight of any unit is entirely up to you. There are few things a commercial manufacturer can assemble or use that you can't. Pretty much all the tools and materials are available.
Lightness is a function of the design and materials you chose to use. Smaller, tighter, designs with fewer add-ons like pouches, zippers, and reinforcements will be lighter. The materials and design you use will be a four-way trade-off between weight, durability and/or function, cost, and ease of manufacturing.
As DIY manufacturer you can take risks that would give a commercial producer a heart attack. To some extent a commercial manufacturer puts their reputation, and profits on the line with every unit sold.
You could simply stitch up a compact tapered treated nylon sack from the most diaphanous ultralight cloth available and have a two-person bivy that would last but one trip and have a bivy that is lighter than any commercial product.
You could start with the lightest sil-nylon tarp made, lay out on your back yard with your trip partner and have someone chalk the outline as you snuggle. Stitch up one seam and hem the top and you have your bivy. It will be about as light as you can get.
Picture a truncated cone shape about 6' long with a minimalist circumference roughly 8' at the top and 5' at the foot made of 1.1 ounce sil-nylon. At something less than 5 square yards of material you might bring it in at less than half a pound. You could save some money buying a sil-nylon tarp and stitching the one seam on a borrowed machine.
You might be able to get enough cloth to make it with one of these for $60 but it is going to be tight:
http://www.campmor.com/outdoor/gear/Product___20068This would be a very confining and hard to use minimalist unit with little margin for wear and abuse but it is hard to imagine one much lighter.
Heavier material, more elbow room, and amenities like a zipper or two, and draw cord would make it more usable and durable but heavier. What trade-offs your willing to make depend on you.