This is undoubtedly upper eyelid ptosis. The right is heavier than the left but here is the thing, the left upper eyelid is ptotic also. This is not caused by "the eyelid skin being too heavy." Fixing just the most obvious eyelid will be very unsatisfactory. What happens is that both eyelid get the same innervation. Fixing the right eye reduced the incentive to lift the eyes open as much and this allows the second eyelid to fall. After surgery the left upper eyelid will look very heavy if it is not fixed at the time of the right side. This can actually be assessed at the time of a consultation. The dilemma of seeing a general plastic surgeon is that they are thinly trained in oculoplastic surgery and don't even have the equipment to properly examine the eyes. For these reasons, I encourage you to see an oculoplastic surgeon. There are many excellent oculoplastic surgeons in Los Angeles. A good place to start is the American Society for Ophthalmic Plastic and Reconstructive Surgery website which has a regional directory which will help you find a well qualified surgeon (ASOPRS dot org).
Two of the most common causes of eyelid asymmetry are either eyelid ptosis or drooping of the eyelid or orbital dystopia which is an asymmetry of the eye socket and eye position. It is difficult without direct examination and additional photos to give you a more definitive answer. The first is more easily corrected and the second is more involved and not indicated due to the mild nature of your asymmetry. Consult with a surgeon to discuss this problem further and to see if you are an appropriate candidate for surgery. Best wishes.
It would appear from the photograph that you have ptosis, perhaps of both upper eyelids however photography can be deceptive. Certainly there is a difference between your eyes. Ptosis is an impaired function of the eye opening muscle, the levator and its attachments. It could be however that there is a basic difference in the eyes, including the bony orbit. You should consult a plastic surgeon who has considerable experience in eyelid and orbital surgery for a complete workup.
Your eyelid asymmetry is something no one notices besides you. Leave it alone. Your eyes are good looking.
The best treatment depends on what your findings are. In your case it seems that you have a few asymmetries, and the best result will depend on what you personally want to achieve. Please see an Oculoplastic surgeon for a personalized consultation.
You appear to have bilateral upper eyelid ptosis (droopy) which is worse on the right eye, making the eyes appear asymmetric. Best to obtain in person consultation from an oculoplastic surgeon.
Thank you for your question and your picture. This is a common problem many people have and there are many causes. For an accurate assessment, nothing replaces an in-office consultation. In this forum, we offer general advice. This is especially true for eye ptosis issues where the problem is dynamic in nature.
Looking at your picture, you a slight ptosis in the right eye when compared to your left. Depending on the degree and its appearance as you open and close your eyes, and when your eyes are fully open, it will determine the best surgical treatment for this. This could range from the right eyelid skin being too heavy and redundant compared to the left eye to a need to repair of tighten your eyelid muscles so that both your eyes open evenly. This is correctable with surgery so you won't have your current problems. Please consult a board certified plastic surgeon or oculoplastic surgeon in your area.