I don't see how anyone who has gotten in shape to do a long brevet hasn't addressed rider weight.
I don't think a Rando bike needs to be particularly heavy - Rene Herse was known for his weight saving innovations. It really comes down to having a bike that will carry what you need, mount whatever stuff you think it requires and deal with road conditions. That isn't going to be a 14 pound bike, but it doesn't necessarily need to be a 35 pound bike. It is hard to talk about this without more concrete numbers - some people would say that a 22 lbs bike is "heavy".
There is definitely a convention for a certain type of bike that seems to revel in its heaviness with grossly overbuilt steel frames, quill stems, steel fender and racks and wheels that would make a downhill racer complain. Those are lifestyle bikes, and Rivendell sells that lifestyle.
Personally, I would ride a moderately light road racing bike that took 28c tires if it could be made to carry the gear I needed, and if not I'd go to an aluminum touring bike with aluminum fork and use medium weight wheels protected by fatter tires if it was really going to be tougher going. Long rides are more pleasant and less fatiguing on bikes that not just climb well but are easy to maneuver and generally handle. Especially if that's what you're already accustomed to.
But I'm not one of those people that believes that racing bike geometry is "tiring" just because they turn easily. Other people have stronger feelings about the deleterious effects of riding a stage racing bicycle over the kind of distances seen in stage racing.