What to Do About Blood Vessels on the Upper Eyelid?

They can be treated with a laser, but you have to wear special contacts to protect your eye from the laser light.

These telangiectasias, as you show on the photo, are small and amenable to treatment with lasers using eye protection or ohmic thermolysis. 

Instead of using Yag or Diode, or any other more penetrating lasers for upper eyelid, I'd use CO2 fractional ablative laser with metal corneal eyeshield protection. Yags  or Diode lasers may penetrate too deeply and cause retinal injury. What CO2 laser  would accomplish is 1) Using thermal energy to get rid of those fine capillaries 2) stimulate collagen production of the upper eyelid so future capillary formations wouldn't be so visible 3) Make your eyes look wider and healthier. :)