One of the students' projects in my class used thick and thin warps alternating, two thin loops and one thick loop repeatedly. It was coming out so nicely that when I got home I wanted to try it myself. I used the warp I had on my frame already, and added some thin cotton seine cord between the thick cotton twine/cord I'd been demosntrating with in class. Here's how the structure looks when stretched. You can see clearly what the thick pair of warps does in the fabric. I love the cabled look between the lacy bits:
But look at all the folds that happened when I took it off tension and sewed it up into a little bag! I think this is so cool, all the movement that it has. It's doing this on its own. I have not tried to block it out. This seems kind of like the "tracking" patterning that sometimes happens spontaneously in plain weave fabric.