Skin sag entirely depends on the person, and their overall health. I've seen some people with skin sag so bad they have 'fins' underneath their arms and others that lost 100+ pounds with no noticeable sag. Some people are complete health wrecks and being overweight is just one problem; others actually have fairly good fundamentals, and just happen to be overweight. To understand this a bit more concretely, think of the difference between a long-time smoker who is obese and spends much of his/her time sick, and a sumo wrestler. If they both lost 100 pounds, skin sag would be very pronounced on the former, but not nearly so much on the latter.
As for how to mitigate it, that is a very complicated question. Skin sag is very closely linked to the 'aging process'; your skin can be considered an organ, and is very sensitive to changes in your overall health. The quick, general answer is that anything you can do to increase your overall health will help alleviate skin sag. That answer, however, is supremely unhelpful due to how general it is, so let me make a short list of pointers.
- Increased hydration (clean water intake)
- Lowered toxin load (less artificial sweeteners, more antioxidant foods like fruits and veggies)
- Losing weight the RIGHT way (relatively slowly, replacing some fat with muscle)
- Proper sleep (reduces load on the rest of the body)
As you've probably figured out by this point, skin sag CAN last forever if you remain unhealthy even after you get rid of your weight. If you get healthier after you get rid of the weight, your body will repair itself and get rid of the unneeded, and likely throughly dead, cells. How fast that happens will depend on how healthy you are and how much sag you have. If you lose weight the right way, at about 2-4 pounds per week max, you should not have a huge amount of sag by the time you hit your target weight, anyway. This is doubly true for you since you're still relatively young. Unless you have some sort of chronic illness, I've got confidence you'll do just fine!