My experiences are similar to Pete's, but of course the weather in a given year may not follow the pattern.
I took a rain jacket and pants, about 6 ounces each. They were important only a few times. It was 41 degrees Fahrenheit and raining on the Blue Ridge Parkway, with not much in the way of available shelter, which would have been pretty miserable without my rain gear. It was rainy and cool one day in Kansas, but I could have gotten through it without rain gear (admittedly with less comfort). It was 27 degrees but not raining at Current Creek Pass in Colorado, so the rain jacked served well as a wind breaker, as it did again when descending Hoosier Pass.
Another touring cyclist in Vesuvius, Virginia was sitting out the rain at Gertie's. My rain gear allowed me to continue on. Sometimes sitting out a rainstorm in some shelter or cafe gets very boring. I waited an hour in Hazard, Kentucky at a church for the rain to stop, but couldn't stand it any longer so continued on, which my rain gear allowed me to do in relative comfort.
Most of the worst rains were overnight when I was already safely in my tent. Daytime rains rarely lasted more than a few hours--I never had an all-day rain.
I would recommend taking at least a rain jacket, but it doesn't need to be expensive or heavy. Almost anything will do.