Ptosis and proptosis
Based on your photos it appears that you have moderate ptosis of upper eyelids. You also have small cheek bones, shallow orbits and your lower and upper eyelids are inserted lower then normal on the lateral (ear) aspect of orbits (negative canthal tilt). In order to correct this deformity ptosis surgery, canthopexy (canthal lift, correction of negative tilt) and possibly cheek augmentation with implants are procedures to consider.
You should consult an experienced board certified plastic surgeon and/or oculoplastic surgeon for detailed evaluation and discuss your options. It is very important to find a good expert since poor surgery can create significant consequences. Good luck.
Drooping of the brows
In these photos, the brows - along with the brow fat pads - are low. This feature is hereditary, but may progress with age-related changes around the eyes. When the brow fat pad begins to slide below the orbital rim as in the second picture (Paul McCartney? or look-alike?), the lids may feel heavy and the lashes may point downward. You are correct that excess skin or fat in the lid is not a problem - in fact, the lids are hollow toward the nose. If the heaviness below the brow is bothersome or symptomatic, then brow lift is the best option. There are many techniques for brow lift - coronal, hairline, endoscopic, or direct. An evaluation with an Oculoplastic or Facial plastic surgeon to discuss options, risks and benefits would be helpful for you when you are ready.