Most of the bivies used by folks here have more water-resistant and VERY-breathable fabrics on the top half like the TiGoat, MLD, etc. with momentum. These have less condensation and weigh less than traditional "waterproof-breathable" ones, like GTX or REI's Elements, etc. They pair really well with a tarp because they keep any wind-driven rain from the edges of your sleeping bag, while the tarp keeps the rain off the main part of the bag. They also help with drafts if you are using a quilt in colder conditions.
If you have a bivy like this, you could probably get away with a 5x8 tarp (look at Integral Designs or Oware, where a silnylon tarp is heavier than spinnaker or cuben but only $54.00). I have a 5x8 ID Siltarp but I only take it in the summer when I really don't think there is going to be any rain. Most of the time, I'd rather carry something slightly larger, even with a weight penalty.
At about the same weight as the REI bivy, you could carry a small tarp and TiGoat bivy and have a more flexible system. Of course, you'd have to add guylines and stakes, but could handle just about any weather in comfort.