Laser or Peels to Thicken Under Eye Skin?

If you have loose skin of the lower eyelids, chemical peels and lasers may be beneficial, but to undergo one of these procedures in an attempt to thicken the lower eyelid skin is ill-advised.
I would consider under-eye fillers with hyaluronic acid (e.g. Restylane) or a cosmeceutical agent containing peptides, such as Prevage anti-aging treatment or Strivectin for the appearance of thicker under-eye skin.
Good luck.

Dear Sunshine,
A few comments.
Ther term "building collagen" is a marketing euphemism for creating scar tissue. When our body is assaulted by a knife, bullet, scalpel, laser or caustic chemical (IE chemical peel) it reacts with an inflammatory reaction which ends up by the deposition of collagen fibers (scar tissue) which HOPEFULLY mold and soften over time. This is NOT always the case.
The lower lid skin has the thinnest skin in the body (as you stated). It is connected on either side to the side walls of the eye socket by thin ligaments. With time and age, the lower lid cannot even keep covering the lower edge of the pigmented part of the eye and slips down, revealing the cornea (WHITE SHOW).
Because of its thinness, as er grow older, the lower lid skin cannot withstand much if any, scarring (a "collagen build up) and ends up being pulled down resulting in an ECTROPION.
So much for "collagen build up".
As to "Would lasers treatment or chemical peels help thicken the skin underneath my eyes, plus have the added benefit of building collagen?" They could. But I doubt you would be pleased with the pulled down lid look such build up may ring with it.
I would suggest you consider LESS caustic ways to enhance the periorbital area such as Botox and Restylane and, if need be, you may need a surgical procedure.
Good Luck.