In this case, surgery is the clear winner

There are a good number of facial aesthetic concerns in which non-surgical and surgical options compete effectively with each other. The type of concern you have with your upper eyelids is not really one of them. By far, the best option you have is a surgical upper blepharoplasty. That’s not to say that if you are completely set against surgery nothing else will help at all. Laser treatments to this area can provide some benefit.

While no surgery is risk free, a standard upper blepharoplasty should be a predictable experience for you and your surgeon.
 

Hope that helps