Treatment for very thin eyelids (purple colored) and tear trough hollowness?

There are available treatments for your concerns, and a picture would help tremendously. For the hollows, fillers are a wonderful option and they can range from Belotero to Fat transfer with pros and cons of each. For the skin trouble, mild resurfacing with lasers/microneedling may be an option for you- more specific details can be given after an examination. 

Without a photo it is very difficult to answer in more than just general terms. Certainly fillers, such as Belotero Balance and Restylane are routinely used these days to nonsurgically treat the tear troughs and dark circles under the eyes with gratifying results. The topical steroid-induced eyelid skin atrophy that you seem to be describing are a different matter, however. Some general thoughts on the matter include the use of low strength alpha hydroxy acid containing cream and, if at all possible (the eczema tendency may limit this possibility), the use of a low strength or gentle retinoid cream. The alpha hydroxy acid helps stimulate new collagen formation and native hyaluronic acid production and the retinoid also stimulates the production of new collagen. Continued use may help somewhat to thicken the thin lids.Additionally, dilute concentrations of Juvederm Ultra XC (which I would use for this in my Upper East Side Manhattan practice and Restylane Skin Boosters, which I would use in my Israel satellite facility) might be injected in small amounts both to hydrate and thicken the eyelid skin and to stimulate additional collagen production. Finally, telangiectasias ("broken capillaries), if present, can be treated with radiowaves. I would strongly urge a consultation with a board certified cosmetic dermatologist with experience and expertise in the treatment of the periorbital area.

As discussed below, you really need a consultation to determine whether the issue can be improved with filler (often an excellent choice--Restylane, off label, and I thin it out with an additional 0.2cc of lidocaine so it is long lasting yet smoother than if it's right out of the vial where it might be a little lumpy for thin skin), or lasers/IPL which can be very effective for discoloration. In very thin skin I often pre treat with ThermiRf smooth which is FDA approved for treating fine lines around the eyes but works by stimulating collagen and serves to thicken the skin a bit.  Adding the filler after the Thermi treatments in some patients is better than injecting the filler first, if the skin is very thin.  In the upper lid both ThermiRf smooth and filler are also good options.   It's essential to see an injection specialist and ideally who is an oculoplastic surgeon so you can review all the options.  There is also a newly described technique where I use a drop of Radiesse (which is white) mixed into the Restylane to take away some of the discoloration under the skin if it's due to bluish vessels.  These are all off label delicate treatments and should only be performed by experienced physicians but the results can be wonderful.Best of luck!