It really looks weird. You may have the eyes problems already. You'd better use the warm compress to make the droopy eyes release for a while. Then you should use some time to go to see the doctor and check whether your eyes get the infection or other problems. You'd better take great notice of this problem.
Ok, from what you said, it seemed to be some problem with your eyes. However, it is not the case at all. From what I know, it might be resulted from something related to your brain, to your neurological system, or cerebral infarction,stuff like that, which led to droopy eyelids, if they have not got traumas. Anyway, it is weird and a sign of health problem which needs to be checked on time.
Well, it is not weird to have this situation. And generally speaking, we have to say that it is normal to have only one drooping eyes. First, you should know that it can be on one-side, and of course in both eyes. In common, a drooping eye can make you look tired and unattractive. For the causes, first, nerve damage can cause a droopy eyelid. But on the other hand, contact can weaken the muscles, which lift their eyelids. In that way, it will cause them to droopy. So you should pay more attention to it.