Well if you're not a
wing
then you're a
feather.
Explanation is basically the same as my other answer (EDIT: which I'm locked out of, I've messed my account up). But it does fit better!
Nice riddle.
EDIT: fits better because
Everything about flight applies equally well to a wing as to a feather. But we say "light as a feather". Also, a feather has more "brothers and sisters" than a wing. And "detaching" is less gruesome!
EDIT (by question poster, adding this detail for clarity of other users):
They pick me Up
And Wonder
They call me Light
We pick feathers up, and wonder about them (children love picking them up). "As light as a feather"
I have Brothers and Sisters
Close, so Close
Together we Serve
That from which we were Born
There are lots of feathers, closely fitting together, on a bird's wing. They serve the bird from which they were born (biologically).
Ah, I am Free
Yet Fastened
And when I am Unfastened
I can no longer Fulfill
My Purpose
Feathers are free as the bird, but they are fastened to the bird. When they fall off, they can no longer serve the bird.
I am used for Travelling
But I am no Burden
I am through which It is done
Birds use the feathers for traveling, it is through which the bird travels. And they nearly weigh nothing.