Howdy---I've been dealing with the too heavy issue for as long as I can remember. The only way I can think of reducing the wt. of your rifle ( only because you really like it the way it looks ) is to get a competent smith to heavily flute your barrel. Fluting a 26" tube, done right, will take over a pound off and move the center of gravity, i.e.: balance pt. several inches to the rear probably to right at the mag where it should be. Fluting also doesn't change the barrel diameter so your stock barrel channel will still fit the barrel perfectly. I didn't know the whitworth had a 26" tube ,mine only had a 24" but that was many years ago.
you'll have to have the barrel re-blued but thats no big deal.
Good suggestions from the other members, but if you really like your rifle, there's only so many ways to do the job!
Good luck and good hunting.
Lj