Treatment of Heavy Eyelids or Ptosis
Excessive eyelid heaviness, or show, is a very common finding. It is important to have a proper evaluation by a qualified surgeon as there are different techniques of correction based on the strength of the eyelid lifting muscles. Most cases of acquired (not born with) eyelid ptosis are due to a stretching of the eyelid lifting tendon. This can be corrected with a small surgery that can be done under local anesthesia. There are two different surgical approaches, but a proper evaluation and discussion with a qualified surgeon are essential to determine your best options.
Upper eyelid ptosis
Photos are difficult to use for evaluation but it looks like you have ptosis in which case surgery can be very helpful not only to improve symmetry but also an experienced oculoplastic surgeon can sometimes bring down fat from up inside the eyelid to lower the appearance of the crease and fill in the eyelids. If you don't really have ptosis, this improved appearance can sometimes be created by using filler in the eyelid.
You have some ptosis of the upper lids, more on the right. If you elevate the lids, you will have less eyelid showing. See an oculoplastic surgeon to evaluate your eyelid muscle function and decide what procedure would be best for you.
Procedures to reduce the amount of eyelid seen
It is a little difficult to tell just from your photos, but it is possible that you have some ptosis of especially the right upper eyelid. I would recommend seeing an oculoplastic surgeon to have your eyelids evaluated. If there is some ptosis present, there is a surgical procedure that can correct that.
Small ptosis correction
The right upper eyelid has a blepharoptosis, meaning to fall down in Greek. More often just called ptosis. You need an assessment by an oculplastic surgeon to measure the eyelids and the excursion of the upper eyelid (legator function) which I expect is good. Then you should be able to have either a posterior approach conjunctiva-mullerectomy where all the surgical correction is done from the undersurface of the eyelid, or an anterior approach where the eyelid lifting muscle is approached from the skin side. The anterior approach is more common in Europe and the posterior approach more common in North America.
The lower eyelid sag is noticeable and the lower lid can be raised slightly by tightening the lid with an operation at the lateral corner of the eyelids called a lateral canthoplasty.
Ptosis surgery to reduce upper eyelid show.
Costs: Ask your surgeon as cost depends on the exact operation chosen for you after assessment.
You should be a very good candidate for ptosis surgery under local anaesthetic.