Why does one side of my face show older signs of aging skin? (Photo)

There is a very common phrase in cosmetic surgery, "Your (breasts, legs, two sides of the face, etc.) are sisters, not twins." It means that everyone has some asymmetry, and the goal of cosmetic surgery is not to make you perfectly symmetric, but rather to bring about harmony and proportion, for a natural-looking beautiful result.
That having been said, when it comes to the face, this is especially true, and there are many theories why:
- most people tend to sleep on one side of their face, squishing that side and creating wrinkles, degrading the fat pads faster, etc.
- Most people drive cars quite a bit, and see more sun exposure on 1 side of the face while driving (look up the sunny side of aging for an article I did on this years ago with an extreme case of a truck driver)
- Our bodies are naturally assymetric, and usually have stronger muscles on one side. Strong muscles will make deeper facial expressions and speed up the wrinkle-creating process
All that having been said, given your young age, I think the real problem here is likely your low body fat percentage. It looks like your face has lost a good deal of its normal fat pads, and that causes the cheeks to sink down the face and flatten out. I think you could very easily correct this in either 1 of 2 ways:
1. Fat transfer - although it sounds like you may not have enough fat for this.... and we want to only pull the highest quality fat from your tummy or love handles, so this may not be a good option
2. Dermal Fillers - I would suggest first doing Sculptra 1-2 rounds. It's a dermal filler that's very different from hyaluronic acid fillers. Instead of adding volume, it stimulates your body to build new collagen. It creates global volume and structure, and you're pretty much the perfect candidate from what I can see in the photos. Then, after the Sculptra, you may need/want some more support just in the cheeks. This is typically where young people store a lot of facial fat, and I think you may benefit from the lifting properties of Voluma there. Just 1-2 syringes should be sufficient. The Sculptra results will be very long-lasting in someone your age, and the Voluma would last around 2 years. 
I would not suggest you try to gain weight naturally to restore facial volume. I think you will be unhappy with how much weight you have to gain in order to see the result you want, but also know that weight fluctuations cause your skin to stretch in ways that tend to ruin its elasticity in the long run.

Thank you for your question and photo. Everyone has some degree of facial asymmetry, and the amount you present is not at all unusual. Asymmetry could be due to lifestyle habits like sleeping on one side of your face, muscular asymmetry or simply aging at different rates. In any case, you can resolve the issue with dermal fillers to fill in your right nasolabial crease. Laser skin resurfacing can also help give your skin a collagen boost and plump up your features. Good luck.

 

Exercise may decrease facial fat as well as body fat, and this may contribute to an aged appearance for some.  Many note that sleeping on one side of the face may accelerate wrinkles and folds appearing to that side.  
You look your own stated age in your photo, not 50, but any uneven area often has many good solutions, some that you mentioned.  
You can easily obtain a free consultation from someone in aesthetic medicine or cosmetic surgery in your area to develop a treatment plan if this bothers you.