Blue eyes have nothing to do with your ability to cry. I have blue eyes and sometimes cry a little too easily. As for the tanning thing Often blue eyed people have fair skin and in that case it would be hard for them to tan. However there are some blue eyed people who have darker skin who tan quite easily.
No, it doesn't affect crying or tanning at all. Usually people with blue or light green eyes have more trouble in bright sunlight ( I do, the sun affects me more than my family members with darker eyes) but how would it affect crying?