According to this study:
"Floppy eyelid syndrome is originally described in obese men with easily everted upper eyelids. Recent studies have found an interesting association with obstructive sleep apnea that has both diagnostic and therapeutic implications; Floppy eyelid syndrome may be a presenting symptom in patients with undiagnosed obstructive sleep apnea , and, in addition, treatment of obesity and sleep apnea may have a favorable effect on the course of floppy eyelid syndrome."
In another recent article in the journal Sleep Medicine, a paper concluded:
"Reported ophthalmic findings in patients with sleep apnea syndrome include floppy eyelid syndrome, glaucoma, and non-arteritic anterior ischemic optic neuropathy."