Why are my eyes very droopy and how can I fix it?

Your eyes are not that prominent. You do have a significant abnormality of the tendon that lifts the upper eyelids. This is caused by a slippage of the how these tendons insert into the upper eyelids. The right side is more dramatic than the left side ( in reference you anatomic right and left)....

For significant improvement, hooded eyelids require surgery if there is enough skin. For nonsurgical treatments: Radiofrequency (Thermage or Venus Legacy/Viva), injectable fillers, and a Botox brow lift can help contour the eyebrows and lift the eyelid skin. I recommend getting a formal...

To achieve more deep set eyes you could try placing filler along your brow bone to give you a stronger brow which will make your eyes seem more set-back or deep set