.....No mine are heavier.Hopefully I am misreading what you've written or I'm not understanding how you wrote this.
On average, when comparing barrels of the same length, contour and bore size, they will weigh very nearly the same (within a couple of ounces). Change any one of the variables and you will discern a difference in weight. The only weight difference I've noted is when someone tries to compare Carbon Fiber barrels to the same contour and length of steel. Dan Lilja used to have a chart or conversion formulas to figure this out before ordering a barrel.
LW barrels are Stainless 50, I was told from a barrel Smith. He won't chamber anymore for me due to time involved because of hardness. He had to slow lathe down and change to a different type cutting fluid to get the finish he was after on chamber before polishing.
My 26" LW barrel tapered to .620 was 1.3lbs heavier than a factory Savage 26" SS barrel with a .920 taper. The 26" LW bull straight taper barrel was 2 lbs + heavier than my 30" Brux straight taper........it made my custom F-Class style rifle so barrel heavy I added 2 lbs to the stock to help balance when bench shooting.
The best barrel I have ever had was a Green Mountain .224 cal. 24" blank with .920 taper. It was button rifled and was cleaner cut than my custom barrels when viewed with a Hawkeye borescope. Better rifling and lands than Brux machined rifling or any of the 50 plus rifle barrels I have viewed.