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If you're not expecting really heavy precipitation or high winds it could work, but you're going to want to use more than just gorilla tape at the corners: You want a network of tape running around the edges and out to all major tieout points and along the ridgeline, so that all stresses are placed on the tape (reinforcing the ridgeline with some sort of cord between the blanket and tape is also a good idea, with the cord taking the actual load). Reinforced packing tape (the kind with fibers running through it) would be lighter and stronger than gorilla tape, as well as having more waterproof adhesive.
Something like that should still weigh less than your blue tarp by a good margin, probably in the weight range of most silnylon tarps. Of course it'd be less durable than silnylon tarps, but it would also end up being a heck of a lot less expensive.
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