What type of plastic surgery can be done on a wobbly chin?

Depends on size.: The treatment will depend on the size of the wobbly chin. Also, if the reason is due to fat or exctra skin or both. If it is mainly due to fat then liposuction would be a good treatment or possibly even weight loss. If it is due to extra skin, if it is not excessive then one could have a nonsurgical option, like ultherapy or thermage. If it is a lot extra skin consider a facelift.

Neck Lift : A "wobbly" chin typically results from changes in your tissue over time that result in loss of elasticity of the skin and tissue of the neck. Excess, loose neck skin must be removed and tightened in order to create a more sharp contour along your neck and chin. This is achieved with neck lift surgery, and requires a long incision around your ear and into your hairline to achieve that goal.

Chin laxity: It depends on how "wobbly". Many times the improvement can be made by a laser liposuction or ultrasound procedure if the problem is not excessive. However many loose chins can only be improved with surgical skin tightening and lifting. I individualize these procedures all the time as there is so much variation on getting the job done.

Neck lift or ulthera: You ma be a candidate for ultherapy for nonsurgical improvement, or a surgical neck lift with or without chin implant . Consultation with a board certified plasti surgeon will help you decide.