Having replaced the barrel on my Browning, I hear you.
Many barrel makers make high quality light rifle barrels.
Just forget fluting a light barrel.
The McGowan 26", Douglas #4 profile in 7mm stainless weighs 3lb 7 oz before mounting. It shoots bugholes with it's favorite loads.
Many short actions weigh around 2 lbs.
The Pac Nor website can tell you about barrel profiles and weights.
Hope this helps.