Does Latisse cause peri-orbital fat loss?

There is no reason that Latisse should cause periorbital fat loss. I would consult with your doctor to determine the actual cause of the fat loss. 

Latisse has never been shown to cause periorbital fat loss.  Bimatoprost (the active ingredient in Latisse) may be associated with periorbital fat loss  in patients who use it daily for many years for glaucoma.  The association with this is interesting and poorly understood but if used as directed it would be unlikely that Latisse could do this.