As this has been a longstanding problem, most likely you have what many of us do - facial asymmetry. Rarely there are medical conditions causing pathological asymmetry - such a Parry-Romberg, but if there is a continued change I would have an orbital and eyelid specialist evaluate you. With regards to one eye almost closing when you smile, I would have an eyelid specialist take a look and evaluate your ocular health to make sure your eyes are closing properly!
There are several assymetries in the pictures shown. There may be a difference in the prominence of the eyes such that one eye is bulging or the other is sunken. In addition there appears to be some eyelid differences which become more noticeable when smiling. It would be important to have an in person or video exam to determine the structure issues such as eye position vs the eyelid movement. There are several possible solutions to improve or camouflage the assymtery. An oculoplastic and orbital surgeon can often evaluate these problems best.
Combo problem requires combo treatment
From your photographs, it appears that you have both ptosis (droopy eyelid) and dermatochalasis (fullness/puffiness) of your right upper eyelid. A combined ptosis repair and blepharoplasty would probably correct your problem. Make a consultation with an oculoplastic surgeon.
There could be combination of right upper eyelid ptosis (droopy eyelid) and right enophthalmos (sunken eye). There is likely pre-existing facial asymmetry with smaller right face area. See an oculoplastic specialist for evaluation and possible treatment.
How can I correct my uneven eyes?
Your eyes definitely do not look the same. The right eye seems relatively set back compared to the left giving it a smaller appearance. You need a full examination by an Oculoplastic surgeon to try to determine what is going on.
Hard to precisely know your issue without an actual consultation.
From a casual look at the photos, the most likely assumption would be that you have ptosis, which is a heavy upper eyelid. While this is the most likely possibility, another potential cause for your issue is enophthalmos. This is the medical term for an eye that sits deeper in the eye socket than normal. A prior history of an orbit fracture on the right side would be consistent with such a condition. There can also be a progressive condition called silent sinus syndrome where inner opening to the maxillary sinus closes due to scaring. This leads to a slowly progressive loss of maxillary sinus volume. The loss of sinus volume corresponds to a gain in eye socket volume. The eye socket sits directly above the maxillary sinus. The first step in addressing this issue is to make a firm diagnosis.