I am born everyday, and always awake.
Everyday with sunrise the sky is born and almost always there are clouds in it. But, clouds are around always, and always moving.
Some times I am plenty, and some times none.
Sometimes there are lots of clouds, sometimes few.
I don't have feet and I travel light.
Clouds have no feet, but are "fluffy and light."
People, few happy, are on me.
Happy people are sometimes said to be on "cloud" 9. Other times we hear about "storm clouds" when people are mad.
And day by day, they want me more.
Depending on the season, people often want clouds. In the winter for snow and the other activities. In summer for shade.
To put the load they don't want to carry.
Here I'm a little short. Maybe, we wish our burdens were light as a cloud? From the OP, refers to storing data on the cloud.
I can't see you as I have no eyes.
Clouds have no eyes, and technically can't see.
But cry I do, day or night.
Rain comes day or night.
For, I am, you see loud.
Lightning in the sky can be very loud. Or (thanks to Rand for pointing this out), see loud, "c" loud, cloud.