If it is fluted, it is probably at least a #3 contour (Weatherby offers only 4 contours and number them 1 through 4) the #1 is very light and normally a muzzle break cant be installed. The #2 is about the same size as a standard sporter weight barrel. The #3 is used on all of there Accumarks and big cartridges up 378 WM the #4s are normally only found on the 460 and some of the older 378s They are about the same as a Sendero Contour.
In my opinion, A #1 contoured barrel has no place in a hunting type weapon. They have only 1 advantage (WEIGHT). They can be very finicky to bullet weight, loads in general, And in magnum calibers they are unpredictable as to weather they will shoot well at all.
At best they will normally be short range weapons. Note: But they look good.
Just because the barrel is very light doesn't mean it wont shoot, just that the odds are not very good that it will. With the right load they can be accurate enough for a first shot hit (Cold Bore)
but after that, who knows where the bullet will go.
This is just My opinion for what it's worth,
J E CUSTOM