Weak Chin - Jaw Surgery Vs. Chin Implant?

While I perform both bony surgery to improve the chin, as well as implants, I generally favor implant surgery. A chin implant is a short, out-patient surgical procedure with few complications. Cutting the chin bone itself is a much bigger operation which I would hesitate to recommend, unless there was no alternative.
As a plastic surgeon with both a medical and dental degree, I have performed many operations on the jaws to move the bones, including the jaws and chin, but surgery on your jaw may not improve your TMJ problems and you should consider that fact in your decision. My gut reaction in looking at your photo would be to opt for a chin implant. If you did a chin implant, you are not burning any bridges, and could still do jaw/chin surgery at a later date.
To simulate what it might look like, I frequently inject sterile water into the patient's chin and you can immediately look at it in the mirror.

In many instances jaw surgery can accomplish both goals. However, traditionally these are different surgical proceduress. TMj surgery typically does not improve chin projection whereas a SSO for malocclusion or sliding genioplasty can definitively achieve chin enlargement. The use of submental liposuction can enhance the result as well.