Fluting a barrel will destroy it unless done just right. It should be done before heat treating. Cutting metal from a barrel will 1, change the harmonics of it. 2. introduce a lot of heat and heat causes stress.
If you want a lighter barrel you can have it rebarreled with a barrel with a smaller taper. Varmint rifles are made with heavy barrels to withstand firing a lot of rounds in a day.
I totally agree with THB get you a good high quality sling with padding.
I have one of these that I move from rifle to rifle. I love it. http://www.timberbutteoutdoors.com/photogallery.html