What causes broken blood vessels in eyelids?

Many causes: Broken blood vessels or bruising on the eye ball which is called subconjucttival hemorrhage. The most important one is high blood pressure that leads to breakage of small blood vessel. If your blood is thin from use of blood thinner then may cause easy bruising on your skin and conjunctiva from minor trauma. Other causes: intense coughing, sneezing, blowing nose, heavy lifting and straining.

Need more info: Could happen spontaneously, and for no reason at all. Rule out rubbing, taking blood thinners such as aspirin, and check blood pressure but if happening very frequently would need to do a workup of the clotting factors.