Doesn't work that way for a few reasons...
The lower profile tires require different steel belts (more of them) to stiffen up the side wall. Different brands of tires are also slightly heavier than others...
Also on my 17's I run a larger diameter and wider tire, 215/45/17 vs. 195/55/15, which requires more material, which makes it heavier. Most 215/45/17's are in the 20-23lb. range. Most 195/55/15's are in the 17-19lb. range.
You can actually purchase the same exact tire in the same size and it will weigh 2lbs less depending on how it is built! A perfect example is the Yokohama Advan Neova AD07 for the Lotus Elise, since the Elise is such a light car and it comes with the AD07 as the OEM tires, Lotus worked with Yokohama to "fine tune" the tire and formulated a specific tire for the car. They found that a lighter car behaves better with a tire which has a softer sidewall (less steel) since it conforms to the road surface better and grips better. This comes at a slight reduction in "load rating" but in the Elise's case this isn't a concern since the car is sooo light.
If you go to
www.tirerack.com and look for the Advan Neova in OEM Elise sizes you'll notice they offer two different "specs" of the tire. In the specs you'll notice the "lotus OEM" spec is 2lbs lighter (and it uses the same rubber compound!)
Hope that helps clarify it?