My 25 year old Wheeler is around 26lbs. My son's more modern X-Cal 6 29er was around 31lbs. I can absolutely tell the difference in the weight when putting them on a bike rack. It's a "woah this bike is way heavier" immediate feel when lifting it up on the truck.Easy answer.
Because it's easier to pedal a 25 lb. bike up a hill vs. 32 lb bike. It takes less energy to do so and makes for a less sore body at the end of the day.
But taking a 2 hours ride on either one? At my pedestrian speeds I don't notice the difference in energy output or exhaustion in taking either bike out. Lets think about the physics. Work is force applied over a distance. For us Force is directly proportional to weight. But I'm not just moving the bike I'm moving myself + the bike. I'm 195 and my bike is 26 so I'm moving 221lbs over the course of the trail. On my son's bike I'm moving 226 lbs. That's about a 2.2% difference the amount of work through the course of the ride. As an amateur I'm not pushing the edge far enough to notice a ~2% change in energy output. I'm sure there are some that are pushing the envelope that hard but it isn't me and probably isn't most of us posting on this board.