I fly without wings,
I cry without eyes.
In me you can store things,
of almost unlimited size.
What am I?
Clouds don't need wings to fly in the sky
Clouds rain without needing any eyes
Cloud servers/services allows storage of large files on the internet
I had originally given the following for the last point, but revised it based on athin's comments and OP's confirmation...
Large things like airplanes are easily hidden inside a cloud, mountains can be cloaked by clouds
The word is
Can fly without wings
Another way to tell someone to "zip up" is "your fly is open"
Can cry without eyes
The wannacry virus works operates with archives or "zip" files
Can store things of unlimited size
A zip file can store files of unlimited size (given the hardware space)
Sort of similar to Phylyps, but it was the first thing that came to my mind.
Water flies when it evaporates in to the atmosphere
Water cries down to earth when it rains
Most of our planet it stored in water, plus anything you put in water just sort of pushes the water to surround it