First off, please understand that I am not a Thermodynamicist. I just read a textbook many years ago, and don't remember very much from it. 'Ok', let's see if we can figure this out...
To keep it simple, let's ignore any units in our formulas. It's really not necessary to consider them to illustrate how the formula functions in a general sense. Also, let's assume that we're considering two identical sized pads (thickness of the pads can be different or the same), or are only concerned with the area of both pads that coincide or are in contact with each other. So if one pad is larger than the other, we're only considering the area of the smaller pad.
To further keep it simple, let's just stick to
R = d / k, where:
R is the Thermal Resistance
d = is the thickness of the material
k = the Thermal Conductivity for that material,
k is a constant that could only be coincidentally the same for different types of material. Not being a materials guy, I don't know if any two materials having the same thickness and area coincidentally just happen to have the same k value when both are subjected to the same temperature differential.
Therefore, to put it a little clearer, k is a constant that is different for each type of material.
Since, for a given material, k is a constant, it will never change for that material. In case you do some research yourself, in some equations a miniscule/lower case greek lambda is used instead of a k; an L for the d - other letter substitutions exist for other equations also.
Therefore, for any given material, the Thermal Resistance, R, is solely dependent upon the value of d (the thickness of the material). Since d is in the numerator, R is directly proportional to d. So, if d increases, so will R.
It's now easy to see that if d is doubled in value, R will also double in value. You can prove this to yourself by making a simple "test case". For example, pick values for d and k that would yield a value of,...let's say..., 10 for R. So, something like d = 20 and k=2. Therefore, 20 divided by 2 = 10, so R would equal 10. Now, double the value of d to 40. This simulates doubling the thickness of the material since d is the thickness of the material. Now doing the arithmetic, R would be 20 and have twice the value if the thickness is doubled.
We could go into further depth regarding how the constant k value known as Thermal Conductivity is calculated, but at this juncture I'm not sure that it is necessary to answer your question.
I hope this info helps.
[Note: If anyone out there reading this would like to comment or correct me on any point, please feel free to help out here. I recall quite a while ago, someone posted an excellent informative post that applied Heat Transfer equations to the heat loss of a human body and how many inches of insulation was required at different temps. Can anyone find it by searching the Forums?]