This is a very common issue. Both of your eyelids are very mildly ptotic (droopy) with the right being slightly more than the left. From a symmetry standpoint, your eyelids are well within the normal range of symmetry. From the photographs it is hard to determine if they have dropped significantly enough for surgical repair. Your use of contact lenses can contribute to the ptosis. You should make an appointment with an oculoplastic surgeon for detailed evaluation in office.
There are many reasons your eyelids can appear asymmetric. First, gradual aging facial changes can cause a subtle difference between the eyes and facial structures, age, contact lens wear, trauma, injury, repetitive rubbing from allergies, thyroid disease etc etc. If you feel it is affecting your vision or progressively changing, it would be best to undergo a thorough history and eyelid evaluation with an eyelid specialist or oculoplastic surgeon. It is helpful to start with your eye doctor to make sure it is not a contact lens or prescription change or ocular surface issue as well.
There are multiple anatomic abnormalities that can result in facial asymmetry. These may include deformities of the orbital bones, eyelid soft tissue and eyebrows. In some cases, they are relatively minor, but in some cases, they may be severe and extremely noticeable. Depending upon the deformity, treatment may or may not be possible.
Your pictures suggest that your asymmetry is probably related to multiple factors. These include bilateral eyelid ptosis which is worse on the right than left side. In addition, you have many findings that suggest boney orbital asymmetry as well.
It's virtually impossible to accurately assess this problem without performing a physical examination. For this reason, it's appropriate to consult a board certified plastic surgeon with experience treating this type of problem. This surgeon should be able to formulate a treatment plan that addresses your anatomic findings and achieves your aesthetic goals.
You have mild ptosis (droopy eyelids), which appears to be slightly worse on the right. This is common and may not be impacting your vision. An oculoplastic surgeon could evaluate you and determine if any treatment is necessary.
You have a ptosis of the upper lids, worse on the right. So the right eye will appear smaller. You should see an oculoplastic surgeon who can evaluate your muscle function and decide which type of ptosis repair surgery would be best for you. You can then decide if you want to do the surgery - it is elective, so depends on how much the droopy lid bothers you.
The difference you are describing is related to ptosis of the upper eyelids. This can be from weakening or loss of the levator muscle or Muller's muscle. It is correctable if it's bothersome to you.
You appear to have drooping (ptosis) of the upper lids which is worse on the right side. It can be corrected with a short outpatient surgery.
If not history of trauma or disease entities than blame it on your genetics! Look at Mom or Dad to see if there are similar appearances...