You can remove the bags under your eyes through a null through incisions under or inside your eyes. Skin can also be removed. This is the traditional method of doing this and improving the lower eyelid area.
You can also fill in the volume deficiency with fillers or some other volume enhancing method. Your lower eyelid has the baggy appearance often from the volume loss that occurs in the cheek area where the loss reveals the infraorbital rim. Replacing this volume can really enhance the appearance in this area with fillers. Fat injections may be the most natural way to improve this area and for a longer lasting effect.
These procedures can be done by Dr Philip Young MD at his Bellevue office near Seattle, Washington.