Something I learned sailing: No matter how wet the weather becomes, the experience can be pleasant if you have the right clothes for it.
Something I learned biking: Don't burden yourself with more equipment than you need.

Unfortunately those two lessons present a conundrum. On a single 1-4 hour ride you can probably survive being wet. But being wet day after day, or getting wet and not being able to remain dry after changing, and enduring that hour after hour, day after day on a tour gives me the inclination to think that the sailing lesson takes precedent. Fortunately there are extremely lightweight options for cycling rain gear, so the peace of mind of knowing you can stay dry when things turn dicey on a tour is probably worth the small amount of additional weight. I'd prefer spending a half pound of my cargo load on that and if I were seeking areas to cut back on weight I'd forego the wool clothing in favor of other lightweight alternatives.