Thick under eyelids/baggy under eyes. (photos)

The eyes are the windows to the
soul. All too often, however, they seem to reveal exhaustion. The very delicate
skin around the eyes tends to get crepey and puffy due to fatigue and stress.
An effective non-surgical option that might benefit you is Thermage, which can
tighten the skin around the eyes. The new and improved Thermage is a virtually
painless, non-invasive (no incision!) treatment that can tighten skin and
stimulate your body to make healthier collagen—the building block that provides
structure to your skin. Fast and easy, Thermage requires no downtime from
normal activities.
Eyelid surgery has become one
of my most popular procedures. If excess upper eyelid skin is hooding the eye
and needs to be eliminated, an incision is made in the crease at the top of the
lid and excess fat and skin are removed. The incisions are closed and sutured
on the underside of the skin. If undereye puffiness and dark circles need to be
eliminated, an incision is made along the lower lashes that will be almost
invisable when it heals. Next, the fat below is either removed or redistributed
and the saggy and crepey excess skin is then pulled up and cut off. The
incisions is closed with tiny sutures, which are removed in four to six days.

the roll you see is the muscle of the lower lid under the skin.  When we smile it becomes more prominent, and in some people it is just larger than in others - called a hypertrophic orbicularis.  If you have a small amount of Botox injected into the muscle it will be much less apparent. 

The roll you have under your eyelashes is made up of your sphincteric muscle: orbicularis oculi. It can be thinned out by an experienced plastic surgeon. Be sure you consult an ASPS surgeon.