I'm glad you found the explanation to be clear since there's a lot of steps to determining all of the weld stresses, especially when it comes to the Instantaneous Center of Rotation Method.
I don't see anything about the methodology that would preclude you from using it with welds that have different leg sizes. The formulas for Δu, Δm, and R all include "w" so you would just use the applicable fillet weld leg size there. I don't know if testing has ever been performed on weld groups consisting of welds with different leg sizes to confirm that the method is still applicable, though.