You can determine the weight of an object by the product of the density, the surface area, and the thickness. It can get a little complicated if the bottle isn't of uniform thickness, but the average thickness is a reasonable approximation. Now, the math becomes simple junior high arithmetic.

Weight (large bottle) = Thickness (large bottle)* density (large bottle) * surface area (large bottle)
Weight (small bottle) = Thickness (small bottle) * density (small bottle) * surface area (small bottle)
weight (large bottle/small bottle) = Thickness (large bottle/small bottle) * density of material (large bottle/small bottle) * surface area (large bottle/small bottle) <>33

the density of material (large/small) equals 1 since we assume both are made from the same plastic.
And we know from before surface area (large bottle/small bottle) = 10

So we can determine which is more environmentally friendly by using your method of relative weights or if we don't have access to a scale or actual bottles we can also use

Thickness (large bottle/small bottle) * 10<>33
Which simplifies to Thickness (large bottle/small bottle) <>3.3

Either way, the large bottle needs to be 3x as thick as a small bottle in order for it to use more plastic (excluding spouts and caps)