With a density of about 125 pounds per cubic foot, I get 0.10 pounds (1.6 ounces) for 10 mil by one square foot and 0.20 (3.2 ounces) pounds for 20 mil, coming close to Colin's calc.
Since boat windows/canopies are using 20-30 mil, I'd be looking at 10 mil or thinner for a tent application.
Cheaper ($3.58 for 54"x36") from a fabric shop instead of a chandlery. (Stamping anchors on things always makes them cost more).
https://www.fabric.com/buy/ap-878/10-gauge-clear-vinyl
That vendor also has 20 and 40-mil clear vinyl. I'd suggest getting a yard of 10-mil and playing with it. Try some stitching patterns and then test your seams to destruction. Consider square windows, rectangular, circular, oval. Rutan's Spaceship 1 used small circular windows which gave a pretty continuous view up close due to the separation of our eyes.
The vinyl is rated for cracking to 0F, so good for 3-season use.
If that region of fabric takes much tension, you could stitch in a cross of thin nylon tape (1/2" width?) to transmit tension from one corner of the window to the opposite corner. Or go with the multiple small windows.
Mostly, we did a good job designing and building our house. I wish, though, that we had a window facing north visible from the master bed. We'd see the northern lights more often if we did.