A "cloud" is the answer for the following reasons that pertain to the above 3 criteria which are clues to the answer:
A cloud can fly without wings because the buoyancy of it's moisture is similar to that of the atmosophere, and thus it will float.
A cloud can metaphorically cry when moisture condenses into rain.
A cloud will cast a shadow wherever it goes and thus there is a slight amount of darkness underneath the cloud.
it can fly without wings
it can cry without eyes
wherever it goes darkness follows it
"Sun" could be the answer.
I have four wings, but cannot fly,
I never laugh and never cry,
On the same spot I'm always found,
toiling away with little sound.
What am I?