Premature Sagging at Age 16?

By your own description your body and your breasts are proportionate (both a bit large), and implants do NOT "lift" sagging breasts, nor do they prevent future droopiness!

Your own breast anatomy has a downward-pointing nipple configuration, and this is entirely normal, though it may not be what you want your breasts to look like. Cosmetic breast surgery (probably a breast lift) can improve the appearance of your breasts, but there will be scars, possible loss of sensation, and the cost, (minimal) risks, and recovery from an operation. So you owe it to yourself to have the surgery when your growth is complete (probably by age 15 or 16 for most women, but once your height and bra size remain stable for a year, assuming a steady weight), and when you are as close as possible to your ideal weight, so your result is the most outstanding one possible.

As others have stated, your best bet is to start on a self-improvement plan of decreased intake and increased activity (a bit of both is best, not some crazy diet you can't maintain) to achieve a healthy, stable, and lower weight. In the meantime start researching qualified ABPS-certified plastic surgeons, and start saving for the surgery that can indeed help you greatly!

But lose weight first, be healthy so everything heals, avoid tobacco and drugs, and get ready for a new you! You CAN do it and we all will cheer you on! Best wishes!

Without photos- it's impossible to give the best answer. Since you are a minor- whatever you do - must have the approval and participation of your parent or guardian. I suggest - you wait until you are of legal age  and then re-assess your family or child bearing goals. A lift may not interfere with breastfeeding but a reduction -might

Since you described
yourself as pretty chubby, it is possible that the weight of your breasts has
exceeded the mechanical strength of your skin. 
That is why your breasts are sagging. 
I recommend The Bellesoma Method, which will transfer the weight of the
breast to the underlying pectoralis major muscle resulting in long term
stability and pain relief.  Vertical
scars are avoided and nipple sensation and the ability to breast feed are
maintained.  Best Wishes,Gary Horndeski, M.D.

In addition to aging, #sagging breasts can result from past pregnancies, genetics, or weight loss which can be present regardless of one's age. Hence, sagging can affect a #teenager if any of the factors other than age, have been present.

It is important to remember that young women can continue to demonstrate breast develop through their late teen years and into their 20's. This will vary from individual to individual. Any discussion of surgery before growth has stabilized (for at least a 12 month period) is "premature."In the interim, it is best to focus on your overall health (diet, exercise) with a goal of achieving your ideal healthy stable weight. These things while not directed at breast appearance specifically can help. Weight fluctuations may exacerbate the perceived problem. It is also recommended that you invest in an appropriately fitting and supportive undergarment.When the time comes, you may benefit from a lift but it is very early for such judgements. Consult with your board certified plastic surgeon, as he /she is uniquely qualified to guide you in your decisions.