(1) What is intended by thick?
A quick look through the literature indicates that what is intended by "thick" is that the material be thick enough that the color of the underlying skin not be discernable. Basically: thickness is a quality that is not sought in and of itself; thus it is neither sought in and of itself nor is it something quantitative. So what follows is that regardless of the "thickness" or the "thinness" of the material: as long as the color of the underlying skin is not discernable, then it is considered "thick" regarding this ruling.
There are few things in the basic literature that strengthen the above. First of all: nowhere do we find it said that the material used for a man's turban or a woman's hijab be of a particular thickness. Regarding a woman's hijab, it need only be thick enough so that the hair and skin that it covers be indiscernible.
Secondly: when giving examples of what cannot be wiped over, a common example is that silken socks cannot be wiped over when worn by men. That the example is qualified by "when worn by men" is quite significant, since from this it is understood that if the silken socks are worn by a woman that there would be problem in wiping over them. The only problem with silk in and of itself is when it is worn by men, since it is unlawful for men to use something the majority of which is silk. As far as I know, silk is thin compared to most other materials, even synthetics. So if a woman can wipe over silk socks provided they meet the typical conditions for wiping over barriers, then it would follow that other materials similar to silk in thinness and rendering indiscernible the color of the skin underneath it would also be acceptable.
For the sake of completeness: there is a weak position in the mathab that making the underlying skin indiscernible is not a condition. But this is a weak position, and should only be used when necessary according to the shari`a.