You're right about the weight. Once you are in pretty good shape your weight is the limiting factor. All of the riders I have seen who make big improvements in climbing have done so with weight loss. It's all about the watts per kilogram.
I'm over 200# and I always do lots of climbing. All of my friends who ride a lot can drop me on the climbs but I can pass the people who don't climb a lot and it surprises them.