I have fat pockets around the corners of my mouth. How do I fix this? Would fixing my weak chin help? Or fillers in cheeks?

Thank you for your question. You are concerned about fat pockets at the corners of your mouth, and are asking if you should remove fat in the area, or add filler to the cheeks and the chin. You add you have always had full cheeks and weak chin, but the cheeks are starting to fall due to aging. You also add that you want a heart-shaped face.
I can certainly give you some guidance based on your photos alone, and in the absence of a physical exam. I’m Dr. Amiya Prasad. I’m a Board Certified Cosmetic Surgeon and Fellowship-trained Oculoplastic Surgeon. I’ve been in practice in Manhattan and Long Island for over 20 years. I regularly perform facelift surgery, and use this knowledge of the facial anatomy for deeper placement of filler in the face, using a technique called Structural Volumizing. This technique can be applied for filler placement in the cheeks, jawline, and chin to add structure to the face, and prevents a soft and doughy look.
I’d first start off by saying what bothers you in the corners of your mouth is not due to fat pockets, but it’s also facial volume loss. You’ve noticed loss of cheekbone projection, but volume loss due to aging also consists of diminishing muscle, fat, and soft tissue. I wouldn’t recommend any removal of facial fat, but I would advise volume enhancement. We can place volume using the Structural Volumizing technique to give your face more structure, contour, chin projection, and help improve the corners of your mouth. I would apply long lasting hyaluronic acid fillers like Juvederm Ultra Plus and Juvederm Voluma to the chin and jawline to give you more projection to resolve the weak chin, and to make the jawline more defined and continuous. Adding filler in these areas will also improve the bulges at the corners of your mouth when you are smiling.
Potentially, filler can also be added to your cheeks to give you the heart-shaped face you desire. However, it is hard to tell if this is needed without an image of your full face. It is likely that cheek projection also diminished with age, but this can be confirmed through a physical exam.
The Structural Volumizing technique is quite different than regular filler placement. Most doctors place filler in the soft tissue space and fat layer, where the filler can migrate to look soft and doughy. The Structural Volumizing technique, also called the Y Lift, puts filler at the deeper foundational level, atop the bone and between the muscle. Filler at this level is much more stable, and looks more solid, so it can provide facial structure. The results are more natural looking volume, that adds more solid, contoured, and defined volume, completely avoiding a doughy look. Longer lasting hyaluronic acid fillers like Juvederm Ultra Plus and Juvederm Voluma last 1-2 years. Since these are still hyaluronic acid fillers, if one doesn’t like their appearance, they can be dissolved with the enzyme hyaluronidase.
I suggest you meet with doctors who are well-experienced in filler placement, preferably a deeper filler placement technique. Your facial volume issues can more than likely be treated without surgery or fat removal. I hope you found this information helpful. Thank you for your question.

These lines are usually associated with volume loss. I think a combination of fillers such as Restylane Defyne and Sculptra Aesthetic as well as a non surgical skin tightening procedure like Thermage FLX will give you the most complete result. 

Fullness around the mouth and loss of cheek and chin volume is a common maturing pattern. Non-surgically it can be addressed with fillers, Radiofrequency  and ultrasound devices like Exilis. Usually combination of procedures is needed for effective  treatment. You should consult a physician in person for a treatment plan.