Bivies are a viable lightweight shelter option, but there are a few considerations that go along with them. (You can obtain some wonderfully-crafted ultralight bivies from online "cottage" makers such as Mountain Laurel Designs, but since I don't have any experience with them, I'm excluding them from what follows.)

First, the lightest of the commercially-available bivies typically do not have bug netting. Of the ones that do have bug netting, there's not enough to overcome the lack of ventilation (more in a minute). If they do have adequate bug netting, like the Integral Designs Salathe (waist-length panel), the weight runs up toward 2 pounds or more. There are some all-mesh bug bivies available - but they aren't very waterproof, as you may have guessed.

Which leads to the second consideration. Personally, I've never used a bivy without at least a 5x8 silnylon tarp, and usually an 8x10. When it's raining, this gives you a place to cook, or to enter and leave the bivy without getting everything wet. It also lets you leave the mesh open during the rain (a shaped tarp, like the ID Silshelter, may even make an all-netting bug bivy a very feasible option.) Of course, you've now added half a pound or pound to your shelter.

So, a really versatile tarp and bivy combo can weigh almost 3 pounds - which is why I eventually quit using my ID Salathe and Silshelter combo. For many years, the lightest tent around still weighed over 4 pounds and, since solo tents weren't as common, you ended up using a two-person tent that weighed 5 or more pounds. So, even a "heavy" tarp and bivy combo like mine saved a big chunk of weight. However, with the proliferation of solo tents (MSR Hubba and Big Agnes Seedhouse SL1, to name two), the weight advantage vanished and I began using tents again because they were more convenient.

Ventilation is an issue in a bivy - weatherproof bivies sacrifice ventilation, so using them in the summer in hotter areas of the country can be a problem, at best, and totally miserable, at worst.

If you want something lightweight, I'd recommend either of the tents I already mentioned. I'd also suggest you look at an even lighter alternative, the Shires TarpTents. Although I've never been able to get the warm fuzzies over them myself, they are well-designed, incredibly light but roomy, well-built and they have armies of fans. I've never found anything objectively wrong with them; I just like my Hubba better for no particular reason. A Tarptent might be just the ticket for what you're planning.

However, if you still want to give bivies a try, REI's Minimalist at $90 or $100 is a really good deal (and I think there's a 20% off coupon code floating out there in connection with the Anniversary sale?) on a fully functional weatherproof bivy that weighs only a pound and has bug netting over the face hole - but nowhere else, so it can get hot in the summer.