It's not just weight, but what kind of weight. If I dropped 10 lbs from my "guads" and my "cottage of wattage" I would be a lot slower going up climbs. While I would be lighter, my power would be decreased as well.
Now we have to define what is a climb. Psimet talks about Blue Mounds. I rode up that a couple of weeks ago from the town of Blue Mounds. I would describe it as a big hill with a bit of a steep gradient at the end. Overall it might have been about 600 feet of elevation gain. Such things can be "powered" up by a bigger guy, like me. It wouldn't phase a TdF sprinter type rider. It is NOTHING compared to a Cat 1 or HC climb in the tour.
I have also gone up climbs with over 3000 ft of elevation gain with stretches of 15% gradient for over a mile in north Georgia and western North Carolina. Now we are talking about real climbs. These make a guy like me (lots of power, but 200 lbs) hurt like hell. On these climbs every ounce you can lose is appreciated.