What will help to define my jawline? Should I try to lose weight?

I'm not sure Kybella would work in your case. I think you probably need to have fat removed from beneath the muscle (platysma) and the muscle reshaped with sutures. This is called a platysmaplasty. In your case, at your age, this could be done through 1 small incision under your chin. It would not usually leave loose skin since the neck skin has a unique ability to "shrink wrap" back on the muscle when it's widely elevated in surgery.

The photographs demonstrate a recessive chin profile, and fat deposits in the neck. Consider placement of a chin implant to augment the chin forward on a permanent basis for better facial balance and proportions, especially from the side profile. The fat deposits in the neck are probably located both above and below the platysma muscle which may require surgery and liposuction. Liposuction can only remove the fat deposits above the platysma muscle, while surgery is required to remove the fat deposits below the muscle which also includes a platysma plasty. The platysma plasty itself significantly improves the Neck line and jawline. No skin removal is required at age 32, and all this can be performed through a 1 inch incision underneath the chin.