The fold under my butt is extremely long, and my butt overhangs. Is there anything that can be done? (Photo)

As time goes on, the inferior gluteal crease tends to flatten and lengthen.  There is no simple fix for what you seek, and it depends on what your other goals are.  Liposuction of the upper thigh, fat transfer, or even a medial thigh lift (if you had loose enough tissue for this, which you don't seem to have) are all potential options.  I don't think lower buttock excision makes sense in your case, and I would avoid any fat-dissolving injections here.  

 Like all body parts, the buttock too has a wide range normal variation. In your case, the majority of your buttock tissue is at the bottom half of the buttock, therefore creating a lack of fullness and projection at the top and a long overaccentuated lower buttock fold.   It's a phenomenon similar to a deflating balloon - if you reinflate the balloon it will perk back up again similarly if you add more volume to the buttock it will perk back up and give you more upper buttock fullness, projection and possibly reduce a bit of the lower buttock fold length and depth.  In my opinion the only surgical option for this that is reliable predictable and permanent is by way of a buttock implant. Please read for more surgical details: Regarding buttock/hip augmentation surgery, let me start off by saying that I currently see at least 2 - 3 patients, domestic and international, per week that failed "brazilian buttock lift" (i.e. the fat melted away after 10 - 12+ months) and are now seeking a more reliable and permanent option (i.e. buttock and/or hip implants). Allow me to share with you some information that you may not hear elsewhere. There are only two proven safe and relatively effective methods for Buttock Augmentation and Hip Augmentation: 1) Autologous Fat Transfer (using your own fat, transferring from one area of the body to the other) and 2) Buttock/Hip Implants (semi-solid silicone rubber implants that cannot rupture &/or leak). Both are options but what it comes down to, like any surgery, is proper patient selection and long-term results. Indeed because at least 80+ % of the fat transferred will melt away within a year, most patients are not good candidates because they lack an adequate amount of fat to harvest. Another tip is that if you purposely gain weight (i.e. fat) for the procedure, the fat you lose first as you get back to your baseline weight is that very same fat that was transferred into your buttock...so don't fall victim to this recommendation. Even those patients that had adequate amounts of fat pre-operatively, still end up seeking buttock implants after a year or so because most of the fat transferred melted away leaving them with minimal result. Although overall using your own fat is relatively safe, it not infrequently melts away unevenly leaving one butt cheek bigger than the other or with dimpling or hard fat cysts. The one serious complication that can rarely (< 1%) happen is "fat embolism" in which some of the fat gets into the blood stream and travels up into the lungs, heart, and/or brain causing serious problems. This complication is more likely to happen with the larger amount of fat being transferred. This is even more likely to happen when using fillers like liquid silicone, PMMA, Sculptra, and hyaluronic acids. Also fillers, when injected in large quantities, have a relatively high infection rate, guaranteed tendency to migrate away from the original area they were injected, and almost always stimulate a lot of inflammation with a subsequent and disastrous amount of scar tissue/hardening.Thus buttock/hip implants become a very good, safe, and long term reliable option for most patients seeking buttock/hip augmentation (at least in my practice). I prefer to insert the buttock implants through a 1 1/2 inch long incision along the inner curve of each upper buttock cheek at the level of the tailbone, similar to two opposing parentheses ")(" (concealed within the crevice between the buttock cheeks) and the hip implants through a ~ 1 inch incision just below the beltline above the hip region. The buttock implant should always be placed under or within the gluteus maximus muscle. In this position, the implant is less palpable, less visible, and does not sag or shift/migrate over time unlike implants placed on top of the muscle. On the other hand, hip implants are placed under just the fascia because no significant muscle exists in this region. However, because they are much smaller and lighter, their likelihood of migration is relatively low. Because all of this, it is extremely important to seek consultation with a board certified plastic surgeon who specializes in this procedure so that the implant placement is precise for both locations. And in this case too, at least in my surgical practice, the infection rate is minimized to

Liposuction of the lower buttock with injection of the fat into the upper outer parts will often improve the overall shape of the butt.Off label use of Kybella injections can also reduce unwanted buttock fat. Skin tightening devices may also be an option including the Cellulaze laser and Radio Frequency devices.  
Fat injections utilized to fill this area may result in undesirable bulges.
Please consult in person with an experienced Board Certified Plastic Surgeon prior to making treatment decisions.