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What does it change?: Removing eyelid skin that has stretched, or moving the fat that bulges under the eye into the hollow below it.
Is there anything short of surgery?: Partly. Filler is used for the hollow and procedures for fine lines. But skin that hangs cannot be removed by a procedure.
Can it be undone?: Surgery cannot be undone. Filler can be dissolved with hyaluronidase.

There are no numbers and no citations in this box. What has been established, and how far, is below.

First, what is actually hanging. A heavy upper lid has three causes, and each has its own operation.

If the skin stretched, it is upper blepharoplasty — the excess is removed and the scar hidden in the crease
If the lifting muscle is weak, it is ptosis correction. No amount of skin removal restores force
If the brow has descended, it is a brow lift. Operating on the lid alone can pull the brow down further

Treating all three as one leads to a smaller result, or a second operation. Telling them apart is clinical work.

Under the eye is a different problem. Lower blepharoplasty does not simply remove the bulging fat; it repositions it into the hollow underneath, because removal alone can leave the area looking more sunken.

And not all darkness under the eye is shape. Pigment and visible vessels are mixed into it, and those sit under dark circles. Surgery can reduce the shadow and leave the colour exactly as it was.

Changing the shape you were born with is under eye shape.

Options before surgery

Used for the same concern but not surgical. These do carry evidence grades.

Moderate evidenceHyaluronic acid fillerInjection
Early researchPolynucleotides (Rejuran)Injection

Operations for this concern

Surgery on this site is not yet graded for evidence. Reversibility is shown in place of a grade.

Lower blepharoplasty with fat repositioningCannot be undone
Upper blepharoplastyCannot be undone