If a festoon was caused by weight gain, can it be reversed with weight loss?

While weight gain/loss can affect how this area looks it is unlikely that you will see the area correct through weight loss.  I encourage you to meet with a board certified plastic surgeon in your area to discuss your concerns and options.

Festoons are created by the junction of the muscle around your eye (orbicularis oculi) and the skin of your cheek. With aging, all your tissues descend and lose volume, and as this happens, the junction between the tissues become more apparent. Weight gain/loss can certainly accentuate these changes, but weight change in the opposite direction will not necessarily correct it. Depending on the degree to which your tissues have descended, the options range from nonsurgical skin tightening (Ulthera, Thermage, etc) to surgical correction (lower blepharoplasty). 

It's difficult to tell without pictures, but it may improve, it may not. Most likely, a combination of treatments would be best to improve this area. I recommend lasers (clear and brilliant, Faxel) or radiofrequency (sublative, viva), co2 resurfacing in combination with well-placed fillers. I suggest getting a formal evaluation with a cosmetic dermatologist. Best, Dr. Emer