I don't weigh my bikes. Every part or accessory on my bike was put there for a good reason, and usually that reason is much more of a priority than the "weight penalty" of using that part or accessory. My bike gets me to work, allows me to have some offroad fun along the way, and haul a load of groceries on the way home. I've accepted that this level of versatility involves a compromise. To torture a car analogy, I'm opting for the versatility of the SUV, rather than the fun impracticality of the 2-seater sport coupe. Even though I don't really care what my bike weighs, when I'm looking at bikes and components, I often take note of what they weigh for reasons that aren't directly about weight. This is especially true of tires and, to a lesser extent, rims. Lightweight tires tend to be more supple and have a better ride quality, which is a priority for me. A lot of the negative associations people have about heavy bikes are the result of lousy-rolling tires. And the weight of a rim can indicate whether it was designed for big hit dirt jumping or for superlight road racing - I'd rather not mix up the two (usually I'm looking at intermediate weight rims). Weights of handlebars and seatposts and derailleurs and such aren't on my radar.
Not giving a damn about weight is a matter of basic physics. The weight difference between a 'heavy' bike and a 'light' bike is typically only a few percent of my robust body weight. Therefore, a few hundred grams here or there is a laughable and negligible change in the total weight of bike plus rider (at least 250 pounds or 113,500 grams, in my case).
Even if I could spend enough thousands of dollars to make a non-negligible change to the weight of my bike, would it matter? For me, the answer is NO. Most of my riding is simple transportation and social bike rides. I'm usually riding in my easy comfort zone, and not trying to red-line my heart rate. In other words, if I want to go faster, I can just pedal faster. I'm not racing against a competitor or a clock, and I'm limited mostly by my desire (or lack of desire) to ride faster, and my fitness level.
But even if I was more of an intense competitor, I could turn the cranks to the limit of my ability on every ride, and weight still wouldn't matter except on prolonged climbs, twisty corners, or when accelerating/decelerating frequently. Riding a straight line on flat ground at constant speed requires no acceleration, and therefore no force (F=MA) except to overcome aerodynamic drag, rolling resistance of the tires, and mechanical inefficiency of the moving parts on the bike. To overcome those losses, a heavy bike with its extra momentum actually has an advantage over a lighter bike.
Here in Minneapolis and Saint Paul, I spend relatively little time riding my bike up big hills. But some people do ride up big hills, where weight has the biggest effect. This velo-news article has a fun infographic that shows the calculated difference of hill climb times with different bike weights and different hill grade (steepness). In a nutshell, the difference between the light bike (15 lb) and the "heavy" bike (18 lb) is just under 12 seconds for a 150 lb rider doing a one-mile climb on a 7% grade at a constant 200W output. Since I'm more in the fat bike world, where weight differences can be more profound, I could easily double or triple the percentage weight savings, but even a 30-60 second difference on the biggest hill I'm likely to ride all year seems like a paltry reward for the investment I'd have to make to take that much weight off my bike.
There's nothing wrong with having a light bike, if it makes you happy, but if you expect that a lighter seatpost (or whatever) is going to give you some measurable performance advantage, you're wrong. Also, I can empathize with apartment dwellers who have to carry a bike up several flights of stairs everyday. There are plenty of reasons to try to save weight on a bike, but, for most of us, performance shouldn't be one of them.