Best way to remove fat from lower eyelids? (Photo)

These days, it's less common to simply remove lower eyelid fat.  It most situations, I preserve the fat by shifting it into the under-eye hollows (also called the tear trough).  This is done from an incision behind the eyelid so there is no visible scar. 

It appears you have puffiness caused by bulging fat at a very young age.   This can be treated by conservatively reducing the fat through a hidden incision inside the lower eyelid (transconjunctival approach) with no external scars.  This should improve your eyelid appearance for many years to come and if done properly will not cause eyelid hollowing.