Juerg, there's more 9/16" tubular nylon here than you'll ever know what to do with. I purchased one of these spools about a year ago and have given a lot of it away to friends for their projects. The dang thing looks like I never even touched it.
funny, just today I made a trip to REI. they have 9/16" "man rated" tubular nylon webbing for climbing. there are both "mil-spec" (6 kN) and "climbing rated" (11 kN), and both are $0.22 per foot! (kN is kilo-Newtons, the breaking strength.)
you might find the same stuff in another real outdoors type store. not sure about Any Mountain, but definitely not in Big 5 or any of those types of places.
West Marine carries 1" nylon webbing but it is rated 3600# and "not for jack lines" which means not man-rated. I suspect the webbing at JoAnn Fabric stores is the same stuff or might even be polypropylene.