Before I started the hike, I made up my mind that I was going to spend most nights in shelters, so I didn't carry a tent. I had instead the Bug Bivy, from Outdoor Research. The Bug Bivy features a very fine mesh top and a bathtub bottom that worked great in even the worst weather. I used it with the green tarp (pictured) except for those rare nights when the stars were out all night, when I used the bivy by itself.
I had thought that it would be good in the shelters, too, if the bugs got really bad, but it was cool enough this summer that they weren't much of a problem at night.
All in all, it worked okay, thanks to the availability of the shelters. If there had been fewer shelters and/or fewer rainy nights, I might have decided to get a tent. (It might seem counter-intuitive, but when it rained, nobody wanted to set up their tents.)
I probably could have found a lighter tarp, as well, but it didn't make a huge difference. Setting up the tarp usually required more creativity than I felt I had at the end of a day's hiking, but once I got it set up, it kept the rain off me and my stuff!