My wife sews webbing with no problem with her machine. I also have a contact with a person that does this in a commercial outfit that makes safety gear, fall protection harnesses, etc. I'll check with her, too. I'll be monday before I can find out.
You need to "burn" the edges where you cut like you do nylon rope, or the cut end will unravel.
They generally sew in a rectange, for 1" webbing, about a 1" square, then sew and X pattern in the middle.
My wife uses a thicker, stronger needle, and dacron thread. But uses her regular machine, hand won't do. She says use a straight stitch but go over it a couple of times.