While I’m not overly obsessed about bike weight, I do a lot of climbing and every kg costs approx 1 min per 1000m of typical alpine climbing. On a big ride I might do up to 4000 m of climbing, so that’s a 4 min loss. That’s not an issue if I’m riding alone, but if I’m in a group it could mean the difference between hanging on or getting dropped. Now if you compare a sub 7 kg bike against a 10 kg bike, then it starts to make a real difference on sustained climbs, especially if you are riding in a group.
To put it in context I can lose about 5-6 kg in weight if I really focus on my diet for several months and that’s when I make the biggest gains on hilly rides. My current bike weighs 8.8 kg with pedals, so I could potentially drop another 2 kg, which would give me less than half of the gain from losing weight. So a lightweight bike is more the icing on the cake and really only significant when doing a lot of climbing.