Can fat grafting (or fillers) under my eyes slightly lift their outer corners?

Fillers, fat, lasers, microneedling/prp helps this area.  I suggest seeing a cosmetic dermatologist with experience.  Best, Dr. Emer.

Without photos it is hard to recommend a procedure.  If you have some hollowing, then filler should help.  Filler placed toward the lateral part of the lid can help to support the lid, and may even raise it up some.  Before doing fat try some filler to see if you can achieve the look you want with extra volume.   

Fat grafting also called fat transfer can certainly be used to improve hollowness under eyes. Results look and feel completely natural and last for many years. A careful exam would need to be done to determine if the added volume under the eye would help support the lower lid and corner or not. 

I would think it would definitely correct the hollowness, but I doubt it would change the rounding of the eyelid along the lateral aspect.  I have seen fat transfer improve scleral show.  You should post photos inorder to get  a better idea.

Without photos it is tough but you may need to have your lower eyelids tightened with a canthopexy and then at the same time maybe do some conservative fat gr5afting to your  lower lids.l

In certain cases volume restoration can minimize scleral show.It will not raise the outer corner of your eyelids. That part of the eyelid is generally anchored to the bone and can only be lifted by surgery.The more detailed description or assessment will require an examination.while significantly more involved another option may be a mid-facelift. This is a very different procedure than a regular facelift.The goal of the mid-facelift is to restore midface volume and give support to the lower eyelids.this procedure was more popular 10 to 15 years ago.More plastic surgeons are performing fat transfer because it's technically a little bit easier and the recovery is much easier.Still if well performed a mid facelift can beautifully restored midface volume.  I have seen great improvement in lower eyelids including scleral show from this procedure.an in person consultation is always required to make an accurate assessment..Best,Mats Hagstrom M.D.