In reply to GraMc:
I'm another very happy Fuji 10-24 user, but like you, I think it's too heavy to take on most climbs.
I also think that there is an optimum width for climbing photography at around 24-35 or possibly 24-50 mm (optical). iirc, APSC 10-24 works out at about 16-35 optical. (Someone correct me, please, if I've got that wrong.) Too wide and there's a high risk of too much close up detail of ropes, feet, etc and the climbing background gets too distorted.
How about a prime? I can't remember off the top of my head what exactly Fuji offer, but I have been tempted by one of their 35mm equivalent lenses. Lighter, a bit less expensive, and there's quite a lot to be said for the discipline of fixed focal length.
Or another option would be the Fuji 18-55, which is good both for wideish angle, and for pulling in more distant subjects. And it's quite a bit lighter than the 10-24, more compact, and not as expensive.