How could I best remove bags under my eyes?

Surgery or lasers. Temporary measures consist of using fillers such as Restylane (dermal fillers) or juvederm. This can help the appearance of wrinkles and bags under the eyes. A more permanent solution would be cosmetic surgery. Also laser resurfacing with co2 laser can help.
Eyebag Severity? Depends on the severity of the eyebags. Some have very large fat deposits which would need surgical reduction. Small eyebags are due to "grooves" or tear troughs which form an indentation from the inner corner of the eye going diagonally on toward the cheek. This groove forms a shadow or eyebag. This can be treated off label with injectable fillers/fat grafting.
Lower blepharoplasty. The bags under eyes are usually the result of fat bulges from the orbite. They can be removed through the inside of the lower eyelids or through the skin with a fine incision below the lash line .
Under eye bags. Under eye bags are a common problem with a variety of potential treatments by plastic surgeons and dermatologists. Most start with basic skin care and chemical peels. Office injections of facial fillers such has Restylane (dermal fillers) may be the next option. Lastly, plastic surgery of the lower eyelid and cheek will help improve the bags.