The problem with case stretching usually occurs with rimless cases fired in a slightly longer chamber. The case gets slammed forward by the firing pin, expands against the case wall, which unless there's considerable oil in the chamber, holds the case body while the case head gets pushed back against the bolt face. As a result the case stretches between the body and thicker head.
In a properly cut belted chamber, with decent brass (and Weatherby brass is usually good) the belt keeps the case from being shoved very far forward. As a result, the head is held firmly while the case body expands to fit the chamber. The only way the case will stretch between body and head is if the belt portion of the chamber is sloppily cut, or the belts on the brass are too short.
If a problem exists between the chamber and belt, then the COW method will also stretch brass, because if enough powder is used to expand the case fully the same thing happens.
I would try one round and see if there's any evidence of case over-stretching. But if your friend had been firing factory ammo with no problems then there shouldn't be with yours.
