You're in luck, I'm an electrical engineer and recognize sheet-rho calculations.
In my experience, the statement would be better said as...
As thickness increases, resistance decreases.
It would be odd to say "as thickness increases, A increases" because variable "A" represents the thickness. It would be the same as saying, "as A increases, A increases" or "as the thickness increases, the thickness increases."
Many years ago, one of the ladies helping a group of us develop the world's first electronic databooks made a useful statement, "don't tell us red is red because it's red." That seems very obvious (indeed, it is very obvious), but we ran into that problem frequently while trying to describe the SGML for the databooks. I believe you're falling into the same trap because you're forgetting that, in application, there's no difference between the thickness of the film and the symbol meant to identify that thickness. When resolved, they both have the same identifying number.