If you do not snore, or have sleep apnea, then you could benefit from sliding genioplasty or any other type of augmentation.
Can you reduce tissue thickness in mouth area? (photo)
you are thin. You have no excess soft tissue. what you are looking at is bony contours. I would focus on the structure of the face with implants and/or fillers.
Excess tissue around mouth - flat cheeks, small chin
The excess tissue you feel is from the lack of tissue support from flat cheeks and small chin.
A chin implant or sliding genioplasty for the chin and cheek implants or fillers will help greatly.
Except that you must first have your facial bones and teeth alignment evaluated.
to be sure you do not need bony re-alignment of the upper or lower jaw.
Can you reduce tissue thickness in mouth area?
You do not need to have tissue removed or reduced in the mouth area. Your chin is weak and would benefit from augmentation. In addition, you could add angularity to your jawline. As for your cheeks, you could add a bit of filler to provide more definition. See the man in the photo attached...he had all of the same issues. I added filler and angularity to cheek/jawline/chin.