Upper Eyelid Hollow? (photo)

Thank you for your question.  The left sided picture that you sent showing a hollow upper eyelid looks to me like you may have a form of ptosis of the eyelid caused by disinsertion of the Levator  Aponeurosis.
The levator  muscle is the muscle that opens your upper eyelids and occasionally the muscle pulls away from or "disinserts" from the portion of the eyelid that lifts or opens the eyes.  This is a common condition and nothing to be alarmed about.  However this condition does thin the eyelid and in my opinion injecting anything such as a filler like Restylane or fat is risky because inserting a needle in this area could cause further disruption of this important lid elevating structure.
I strongly suggest that you consult a plastic surgeon who is certified by the American Board of Plastic Surgery who specializes in eyelid surgery or an Oculoplastic surgeon who is certified by the American Board of Ophthalmology.
Reattaching the levator muscle to the lifting mechanism of the eyelid is a straightforward and simple procedure if performed by an expert.

Upper eyelid hollowness is a dramatically underappreciated, yet incredibly important component of aging in the eyelids. With normal aging, our upper eyelid fat pads tend to retract and expose this upper lid hollowness, those with “deep set eyes“ are especially prone, and unfortunately old-school upper eyelid surgery that is overly subtractive can artificially create this hollowness early, actually looking worse than it did before surgery - the before and after photo in the link below resulted from overly subtractive upper eyelid surgery with another surgeon, and you can see the results after revolumization of the upper lids. Correcting this hollowness can happen with filler injections into very specific planes of the upper eyelid, or transposing and rearranging the upper eyelid fat pads to provide fullness, as you see in this surgeon’s view video, borrowing the excess fat to move into the areas lacking fullness!

 

Upper eyelid hollows respond well to the injection of volumizing fillers, such as Belotero Balance. Belotero Balance, a hyaluronic acid based filler,has the advantage, due to certain unique aspects in the product's manufacture, to allow it to be injected even in thin areas around the eyes with little concern for the development of a bluish discoloration of the skin seen with other hyaluronic acid injectables that may occur as a result of light scattering. Although I prefer Belotero for this purpose, Restylane L and Juvederm UltraPlus XC have likewise been used successfully for this purpose. The cost will vary according to which material is used and the precise amount injected.

In the hands of an experienced injector, the replacement of volume in this region fills out the hollowed area restoring more aesthetic proportions between the upper eyelid and the lower portion of the brow.  If desired, a test injection of a small volume of salt solution may be used to give an approximate idea of what the final result might look like following actual treatment. Treating areas around the eyes should only be performed by physicians with considerable experience in injecting this location.

Improving upper eyelid hollows with injectable volumizers seldom takes more than five minutes per side.