Mid thirties corner of mouth skin fold, what are my options?

There are several options you have to correct this problem.  Sagginess around the corner of the mouth or in the lower face is virtually always related to the cheek (malar) fat pad.  I rarely address the lower face without making some correction to the midface and lifting the cheek area.  In your case because you describe your face as "chubby" you do not want to add volume to your cheek, however there is a way to do a lateral lift to your face with filler that will actually make the appearance of your cheek fullness less.  At your age this is the preferred method of treatment that I use, a nonsurgical face lift using filler.  It takes a skillful injector to understand this technique, especially in a patient who has fullness in the cheeks, so be cautious in selecting your doctor.  Then, after doing the lateral lift if there is still a need for correction in the lower face that can be done with filler locally in that area.  I would also like to mention that Ultherapy is an effective treatment to tighten and lift the lower face and jawline and combining these treatment options can be quite effective and achieve a longer term result. 
Thank you for the question.  Hope that helps.
All the best,
Dr. Flashner

Hi- great question. It is hard to tell based on just one photograph from a side view, but you likely have a deepening of what is known as the "nasolabial fold" which is that line of skin you see going from the corner of the nose down to the corner of the mouth and then down onto your chin. As we age, this fold gets deeper and more prominent. This is seen in many people, regardless of their weight or the "chubbiness" of their face. 
There are multiple options to correct this. Fillers may be used to soften the fold and make the blending of your face more balanced. Or, the fillers may be applied to your cheeks to add volume which will naturally lift the tissues of your face and help erase the fold. However, if you are concerned about the chubby appearance of your face then you may not want the additional volume here. Finally, a facelift procedure can surgically help with erasing these folds and is the most effective option. However, you are quite young to have this procedure done, and it is the most expensive option while requiring significant recovery time. 
You may consider seeing a board certified or board eligible plastic surgeon to perform a full facial analysis and to discuss appropriate treatment options in person. 

Looking at your photo, it is clear that you have beautiful features, with nice mid face volume and full lips. In my opinion thread lifting such as  instalift  or novathreads can be very precise option for you. I am opposed to fillers in the lower face in your case. I would highly recommend you to obtain a consultation with an experienced  aesthetic physician/surgeon.  Skin tightening procedures such as Ultherapy or RF microneedling can define the jawline and tighten the submental area.
Best wishes
Dr. Shanthala

Ematrix RF, Exilis tightening with Ultherapy, and fillers can help reduce the prominence of your marionette lines. Best, Dr. KaramanoukianLos Angeles

There are a few options: Ultherapy to the lower face can help lift & tighten the area. Dermal fillers such as Juvederm can filler the area below disguising the fold. I would recommend a combination of the two for the most natural result. Be sure to schedule a consultation with your nearest experienced Ultherapy provider & injector. 

Thank you for
your question and for sharing your photograph Jup555. I understand your
concern. Fillers are used to restore lost volume in and enhance the appearance
of the face.The lower face is a common area that we address for rejuvenation. Specific concerns include nasolabial folds (the wrinkles that go from the sides of the nose to the corners of the mouth), marionette lines (the wrinkles that continue from the corners of the mouth to the jawline), the jowls, jawline definition, and the double chin. In order to address these concerns it is important to understand the causes of them.Over time there are structural changes in the face that occur with age. The bony structures in the mid-face move downward and the fat pads get smaller. At the same time the levels of collagen, the protein that provides a firm and youthful appearance, decrease. Together these lead to the appearance of the aforementioned signs of aging. Additionally the double chin is caused by age, weight gain and genetics.To address these concerns a number of treatments options can be used and I find that a combination approach works best. Fillers such as Voluma can be placed in the upper cheek to restore lost volume in the mid-face. This will pull up on the lower face, providing a lift to address all of these concerns. Additionally it also serves to restore the youthful apple of the cheek, which is also lost with age. We assess the results of Voluma two weeks after a treatment once the swelling has subsided. At that point more product can be used if further enhancement is desired. Alternatively a filler such as Vollure can be placed directly into the nasolabial folds and marionette lines. To stimulate collagen I recommend fractional CO2 laser resurfacing for my patients. This treatment works by generating thousands of microscopic holes in the skin and generating heat, which stimulates the skin to produce its own natural, new, fresh, and healthy collagen. This will tighten the skin and pull the lower face up. Other skin tightening treatments include infrared light, other lasers, radiofrequency, and ultrasound. Botox can also be used in the lower face and neck to relax muscles that pull downward on the lower face. The depressor anguli oris (DAO) is one such muscle in the lower face that can be treated. This muscle pulls down on the corners of the mouth, leading to a sad face appearance. When this muscle is relaxed with Botox the corners of the mouth can be elevated by about one millimeter. The platysma muscle on the neck pulls down on the skin in the lower face. When this muscle is relaxed with Botox it can improve jawline definition.Kybella is a treatment that can address the double chin. Kybella is the first and thus-far only FDA-approved, non-surgical, injectable treatment for the double chin. The active ingredient is used in the body to digest the dietary fat. When injected into the double chin Kybella will dissolve the fat and it is naturally eliminated by the body over time. A series of 2 to 4 treatments is recommended, sometimes up to 6 treatment. I treat my patients at 3 month intervals. Swelling occurs 100% of the time and can last 1-2 weeks. Therefore it is important to time treatments around special events. Improvement is seen in removal of fat slowly over time and thus patience is important. As the fat decreases improvement in jawline definition is seen as well.While it is difficult to make an assessment without a formal in-office exam where I can examine the face from different angles and observe various expressions, if I had a patient who looked like the person in this photograph I would say she is likely a good candidate for all of these treatments.
Please
consult with a doctor for specific recommendations.  Good luck!

There is no one answer for this. Whatever you choose, I would suggest a treatment which is going to give you lift to reduce the heaviness at the mouth corners rather than directly injecting them. You could try thread lifting, Ultracel, Ultherapy, facelift using dermal fillers. I find a combination approach works best so a little bit of each. 

Small amount of Botox at your jawline, and filler injection should improve that. It may not make it perfect but it should definitely help