By hand works good, but won't look as good as a dialed in machine stitch, but with black webbing and black thread who will notice?
Dialing in the sewing machine for heavy webbing might take longer than doing it by hand. I have used a heavy duty(not commercial) Singer machine for sewing both flat and tubular webbing. Get the largest needle available for the machine, with a large thread hole. I believe a ball point needle is what worked best for me, it doesn't cut the fabric the way an ordinary needle does. Use thick thread, I think nylon upholstery thread, making sure it has a smooth feel, so it won't jam in the machine. For what you are talking about, a regular stitch will be adequate, but if you want a lot of strength, do a zig zag stitch, but expect to do some practising before you have good results.
You might be surprised at how good a job can be done by hand, with just needle and thread.