I thought a lower profile tire has a thicker sidewall because there is less air to support the weight of the car.
Let's take this physics a bit further to the tire.
At rest, all forces balance. So the force the mass of the car exerts on the tire must be equal to the force the tire exerts on the car.
If I am not mistaken, this force, or at least some of it, is measured as the air pressure in the tire.
If we have a tire with less interior volume (our lower profile 18 in this case) I think it would have to operate at a higher pressure to support the same car mass.
So I'm thinking the sidewalls must be thicker in a lower profile car.
But I could be wrong here

TB