I did exactly this as an experiment and spent the night in the backyard. I spent quite a good deal of time making the reinforced corners and set it up in a half pyramid like I would my 5×9 silnylon tarp. It was too small in this configuration so I changed to an A-frame with the four corners tied out. Looked pretty promising at first. But as the night went on the material started to stretch until and it became increasingly less taut. eventually a mild wind came up and the corners started to rip past the reinforcements until it simply failed. So my experience was that it didn't work because the load doesnt spread out like other materials.
Here are a couple of cheap solutions that I have tried that did work:
1) Shower curtain from the Dollar Store. These are a roughly 12 ounces. The ones at the non-dollar stores are heavier and more expensive. I tapped grommets into the four corners an one center on the side to set up like a half pyramid. Only issues is that you have to find an "Extra Long" size because the standard was only 6 foot long.
2) SilNylon can be found relatively cheap. Buy three yards and just roll and sew the edges. Add the tie-outs and tack them in. If sewing is intimidating you can use grommets instead. It costs weight but you can also roll the edges in duck tape as an alternative to sewing. The goal is just to stop the edges from fraying.
3) Once in a great while I will find cheap versions of the blue tarp in 5×7 at our local hardware store. This is much thinner and lighter than the REI and normal blue tarps. I think the painters request them. But they are much cheaper, $2.50, and much lighter. Though I have only seen them in one size; 5×7.
4) If you can find a used tent or throw away tent, you can repurpose the fly with a little modification. Pretty simple for most flys, but they are usually heavy material. I found a tent without poles at the local thrift store for $5.00 that had a could moderately light fly with it. Gave the tent away and cut the fly in half and sewed the edges. Two tarps for $5.00.
I live in fairly dry country so tarps for me only see light duty and about 2/3rds of the time just get used as a ground cloth. If a light rain comes in I will just roll up "burrito" style to keep the bag dry.
One final alternative. I didn't want to spend money on a bivy sack and bought the AMK bivy that is made out of the same material. On sale it was very cheap. I have used it a half dozen nights and it has worked fine. Waterproof, adds additional heat, fairly light and packs up reasonably small. Like the blanket though it is pain to pack back up once unfolded.
Happy hiking.