It can be a hit or a miss. Are you confident of your ability to calibrate the device in a way that counters the existing asymmetry fully and nothing more, instead of merely transforming one kind of asymmetry to another? Simply pulling the weaker side harder may cause the surrounding musculature to compensate in anatomically unfavourable ways. In an ideal situation, asymmetrical pulling could be helpful, but without getting the spine, the palate and the center of gravity of your body in alignment with each other, it's probably not productive to focus on facial asymmetry at all.

Thanks Progress! I am confident using the facebow with multiple elastics, and external anchorage points on my helmet, which can slide up and down to adjust the tension, that I could feasibly set it to pull up with say 250 grams on the right side elastics and only 150 grams on the left side elastics, and then maybe angle the elastics pulling forward a little to the left to compensate for my midline deviation. However, I think I'm inclined to agree with you that unbalanced pulling has the potential for unforeseen complications. In my mind, pulling evenly on all of the elastics will still counter the asymmetry because parts of the maxilla farther from their ideal position should have less resistance to shifting. Does that make sense?

Another point to mention: If I set the anchorage points at the same height on both sides of my helmet, the side of my maxilla that is canted lower will automatically get more traction because the elastic will have to stretch farther to reach it. I will have to lower the anchorage point on my right side to get the same level of tension as my left side. Maybe it makes sense to just keep the anchorage points symmetrical rather than trying to keep the tensions symmetrical.