Just to clarify, by "bivy" do you mean a bivy/tarp combo or just a bivy by itself??? There is a huge difference in weight and function between the two.

For the sake of this discussion I'll assume it's just a simple bivy, by itself with no structure e.i. poles. Some bivy/tarp combos weigh more than some tents. Then of course there are "bivy" tents like the much discussed Nemo GoGo. Is that shelter really a bivy or a small tent? It's complicated and direct comparisons are not simple.

Bivies have their advantages......and limitations. I will always reach for a bivy first unless I expect bugs, rain, cold temps, long nights or high winds. For me those are a lot of limitations. Call me crazy but I like to be comfortable at night. So if conditions are not ideal for a bivy I use something else. But I love it when I can get away with one. There is nothing like sleeping under the stars and packing up camp is so simple....I just stuff my bivy, with my bag/quilt still in it, into the bottom of my pack. Done. There is nothing more simple and for me simplicity is what it's all about when it comes to gear.

Notice I use the words "for me" often? Like I said it's not a simple comparison and it all comes down to whatever butters your popcorn.
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If you only travel on sunny days you will never reach your destination.*

* May not apply at certain latitudes in Canada and elsewhere.