Laser or Peels to Thicken Under Eye Skin?

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.

Dear Sunshine26,
Chemical peels and lasers will not thicken your under eye skin. Actually, nothing will thicken it. However, if the thin skin bothers you because you can see underlying blood vessels, I recommend considering a hyaluronic filler in that area. It will hydrate the skin and by bringing in water, it will plump and fill the area and thus lift the under eye skin up and make it appear "thicker." In reality, it will help conceal the vessels under the eyes by tenting the skin up. I recommend finding a board certified dermatologist in your area who has used fillers under the eyes.
Good luck,
Dr. Mariwalla