I wove several yards with my single-ply, spindle-spun, recycled plastic (from newspaper sleeves and dollar store picnic tables), using baling "twine" as the warp. I made seat cushions for the deck. I used fishing line for the parts of the "fabric" that needed to be thinner - the fabric that becomes the hem - for instance. With the leftover piece of fabric, I made a water bottle holder that I have used daily for 2+ years. It is showing signs of wear, but I have been impressed with how long it has held up so far.

I used the baling twine for the warp because the recycled stuff was too spongy, it wanted to stretch apart (particular the newspaper sleeves). I was also worried about how fast the plastic might disintegrate, especially in the sun. Otherwise, it was inelastic: you have take up, but no shrinkage. It does not have to be rug-weight, nor plain weave. You might need to weave it with a very firm to hard beat.

Project notes are posted at Ravely here:
https://www.ravelry.com/projects/SallyOrgren/plastic-yarn-project

Another consideration: Heddles

You have to make sure the material passes through the heddles you have.

And if a warp thread breaks and you need to knot on a new one - will the join fit through your heddles.

I once wove a "coat" using carpet warp for the warp and strips of plastic bags in the weft. It was for a fun fashion show. The coat hanged in my studio for about 5 years but I had to discard it because the plastic started to disintegrate and shed.

Plastic rugs were a staple in Swedish kitchens when I was a kid. I think they may still be, but the designs are better. The ones I remember from back then were mostly in Rosepath. We have some in the summer house there that are probably 50 years old. The plastic is just in the weft, and it’s not recycled newspaper bags or whatever. They’re a lot like the Swedish rag rugs. Google “plastmatta” and you’ll see a bunch of them. 

At least 30 years  ago I wove picnic placemats using carpet warp and whole wheat bread wrappers for their color. They are still in great shape.

I have woven various tote bags with plastic bag strips (and sometimes used a piece of bicycle innertube for the bottom). I have found that red and orange newspaper sleeves (and perhaps other types) disintegrate after several years, with or without sunlight. Other colors are lasting for years seemingly unchanged.

The design and execution looks great, Isabelle!

Was it water resistant if not water-proof?