Evening. I have not shot a .300 Weatherby Magnum but do own a .300 RUM (Remington 700 BDL with 26 inch barrel and muzzle break).

I've gotten good results with 95 grains of H-1000 behind a 180 grain Nosler Partition. I've shot 1" groups at 100 yards. I use CCI 250 Large Rifle Magnum primers

Using the Nosler Reloading manual, 5th Edition as a guide, extracted the following data for the .300 Weatherby and .300 RUM.
180 grain bullets and max loads for all examples below.
.300 RUM
IMR 4350* 82 grains Muzzle vel. 3187 fps
RL 22 87 grains Muzzle vel. 3220 fps
H4831sc 88 grains Muzzle vel. 3205 fps
AA3100 88 grains Muzzle vel. 3206 fps
IMR 7828 89 grains Muzzle vel. 3229 fps
H1000 96 grains Muzzle vel. 3225 fps
* Most accurate load tested

.300 Weatherby
IMR4350 76 grains Muzzle vel. 3088 fps
RL19 79 grains Muzzle vel. 3198 fps
IMR4831 76 grains Muzzle vel. 3028 fps
RL22 80 grains Muzzle vel. 3132fps
AA3100 77.5 grains Muzzle vel. 3050 fps
IMR7828 84.5 grains Muzzle vel. 3185 fps
H1000 89 grains Muzzle vel. 3146 fps
H870* 92 grains Muzzle vel. 2970 fps

As you can tell the .300 RUM is a bit faster and will also have a bit more energy.

Regards