Is it normal for the dominant side breast to remain higher and fuller 6 weeks post op?

At 6 weeks, you are about 35 percent settled, shaped, softened, dropped and fluffed. "Drop and fluff" refers to the fact that as the skin stretches and the muscles relax, the implants move down and out slowly – about 1 percent a day. It’ll be about six weeks before they even begin to settle down, but they’ll be close to 80 percent settled and softened at three months. Watching their progress is like watching your hair grow. You don’t see a difference in your hair growth daily, but all of a sudden you need a haircut. 
Be patient after surgery. Give yourself a few months before making a judgment about your surgical results. You won't know the outcome until then. 
Dr. Ted Eisenberg, Board Certified Plastic Surgeon and Author

Dear GymBunny487,I understand your concern and it is quite normal to be concerned about the outcome following a breast augmentation surgery. However, you are still in the very early stages of the healing process.Your will need to be patient at this moment and follow what your surgeon has instructed you to do post operatively.At the early stage of the healing process, the tissues around the implants are still swollen. Once the swelling subsides and the implants drop to their final position, you will be able to see the final result of your breast augmentation surgery.Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

It is not uncommon have some asymmetry in settling after breast augmentation. Give you body a chance to completely heal. I wouldn't have recommended any lifting of weights until after 6 weeks. See your surgeon if you have ongoing concerns. Take care

It is not always the dominant arm that takes longer to drop into position.  If your surgeon created equal pockets on both sides the implants should even out over time and drop into place.  It can be frustrating to wait this out but be patient and im sure you will be happy with your results.  

It is quite normal for the breast implant placed into the smaller breast to take longer to drop into place and to appear higher in the first few weeks after breast augmentation.It takes more time for the implant to stretch the smaller breast to allow the implant to drop.You are still early in recovery and your implants will drop further as time goes on.However it is best that you see your plastic surgeon for an in person examination and ask if you may begin breast implant displacement exercises.