The larger the pizza, the smaller the ratio of fixed width perimeter to center. If the area of the perimeter were to maintain a constant ratio to the total area, it's width would have to increase in proportion. That applies to any 2D shape, not just a circle or square.
In fact, the calculation in op is wrong because a 16" pizza isn't merely four times as large as an 8" pizza. The 1" crust makes the 16" really a 14" while the 8" is really a 6". 14^2/6^2 = 5.44 times as large.
b: If you were to say anything like that in the USA, you'd be reported to the TSA for un-American activities as soon as anyone heard you. And the NSA would hear you, even if you said it inside your own head. So bring a 100ml or smaller bottle of lube with you for the probe next time you fly.