Will having the fat pads removed from under my eye cause hollowing over time?

Your photo is taken at an odd angle, and you're smiling, so it's difficult to see exactly what would work best for you.  From your photo, you appear to have fat prominence on your right side alone, so perhaps surgery on that side is all that's needed.  A transconjunctival approach through the inside of the eyelid would be the safest.For many individuals, especially those who have fat projecting at a young age, fat removal in blepharoplasty is both appropriate and necessary.  I

 Thanks so much for your question. If the fat you remove from your eye is not over done it should not look hollowed out. However there is always a chance but if two much is resected that you may be hollowed out.   Be sure to be see a board-certified plastic surgeon in order to get the correct diagnosis and plan.