My Ultimate Shadow gained a full pound with a Boyd Stock in Grey Laminate. The McMillan Edge will add more I believe.
The Edge stock will be about 1/2 lb LIGHTER than factory, not heavier. You should be 6.25ish with a bare rifle.
This is a Classic, not the Ultimate Shadow, but they will be about the same. The US already comes with aluminum bottom metal which should be close to the same weight as my PT&G bottom metal.
A 30-06 is on a long action and will be a few oz heavier, both have 24" barrels.
Model 70 Classic Sporter 300 WSM
Edge stock
Talley lightweight mounts
Leupold VX-2 3-9X40
PT&G alumimum bottom metal
7.5 lbs as pictured