One of the things I go back and forth with is the question of how much weight matters. It's a funny thing, because it's the most objectifiable thing on a bike. Impressions of geometry and handling will vary from person to person, stiffness can be quantified but more is not always preferred for every rider or circumstance, aerodynamics are debated and argued in various ways, aesthetics are a whole other kettle of fish, but put a bike on a scale and there's only one number that's going to come up. All else being equal, the lower that number, the better.
In a world where your like or dislike of a certain golf club is as related to its sound as to its performance, and where cyclists may not have the breadth or depth of experience with different bikes to be able to really pin down their likes and dislikes in the way different bikes handle, it's not unusual that people would place a lot of importance on something that is as readily quantified as weight.
On one hand, I think that perhaps the way that weight's effects are calculated to a racing cyclist understate its importance. Sites like Analytic Cycling allow you to plug in weights versus coefficients of drag so that you can see that, in general, aero does indeed trump weight. But aero benefits are measured in a static wind tunnel, and as you can see if you look at charts and graphs from various wheel companies, even the wind tunnel benefits are hard to nail down. Put them on the open road and it gets fuzzy indeed. You'd have to have your head buried pretty far in the sand to deny that there are valuable benefits available from aero equipment, but to quantify it is rather difficult. Part of this comes from manufacturer claims - the chuckles about the new aero cranks that save you 20" over a full Ironman course (winning Ironman bike splits are roughly 4.5 hours, so this represents a .1% improvement) were pretty loud. So it's hard to know just how much benefit you are getting from aero equipment. You know you're getting some.
On the other hand, the static way in which weight is measured probably understates its practical effect just as the wind tunnel likely overstates practical benefits of aero gear. Most calculations talk about static grade, constant speeds, etc. That doesn't line up at all with most of the climbing experience I've had - grades constantly change, attacks come and go, etc. Even on flat courses, you are constantly changing speeds. I'm guessing that the difference between say a 1500 gram set of wheels and one a quarter of a pound heavier will leave you with more than .1% extra in the tank at the end of the race.
The question is of course one of degree. People chase weight to pretty crazy degrees. On this boat I used to sail on, we had a saying - "grains of sand." What this meant was that if you added up enough tiny little grains of sand, you'd eventually wind up with the Sahara desert, so we were always looking for the small gains. No one carried any superfluous stuff when we raced. But I recently read a comment somewhere that called 10 grams of difference between two sets of wheels a notable difference. In my mind, I struggle to call a .7% difference in weight between two sets of wheels notable. Wheels aren't grains of sand - they're often or even usually the heaviest component on the bike. This apart from the fact that a 10 gram difference is WELL within the weight variance tolerance of any wheels.
Bikes used in road races aren't allowed to weigh less than 14.8 pounds. They often do, since when was the last time an official weighed a bike at a race, right? I know a lot of people get their bikes down to like 13 pounds, and there are multiple websites devoted to the practice of getting your bike down to the lowest weight possible.
Weight is something that we always look at every time we evaluate something, and we recently chose not to go ahead with some new rims because we thought their weight penalty outweighed the benefits they brought. Soon enough I am sure that we'll have the need to evaluate weight versus other factors in other products, and despite weight's objective measurement, we will have to evaluate it subjectively in the mix of other factors.