As a climber, you aren't going to end up on the ground due to nylon webbing stretching. Nylong webbing can stretch ~30% at breaking strength
, which is stretchy, but we're not talking shock cord here. The properties of the webbing are such that the stretch should occur as soon as weight is placed on them. It's not a slow creepy sort of stretch that would cause you to end up on the ground overnight. It may stretch a little, but really, not that much. (Unless you are hanging from trees that are 50 feet apart or something.) Granted, the climbing webbing is WAY heavier than the regular, static polypro stuff that most people here use. Climbing webbing is what I had laying around in my earlier hammocking days, so that's what I used, and I never ended up on the ground.
Also, climbing gear uses bar tacks, essentially very tight zig zag stitches in multiple rows, to create closed loops for their gear. They have commercial machines with special bar tacking attachments to do it in the strongest way possible, but for our purposes, several rows of tight zig zags should be strong enough, if my gut serves me right.