Shaving has really no effect on hair distribution, weight, or any other factor. Hair growth is dictated by many, many factors, including, but not limited to, steroidal and nonsteroidal hormones, cytokines, and nutrition, but shaving has been shown not to be one of them. Linked in the sources is a study in the Journal of Investigative Dermatology from 1970 that performed a study on some young men where one leg was shaven and the other untouched. They found no difference in any of the factors they were testing! That's about as definitive proof as you would need, considering studies like this where experimental subjects are their own controls offer the best statistical power to find any possible difference! There is a similar study from 1928 with the same result, but I was unable to find an abstract or text.
How might some have thought it to be true? Well, hair grows with a naturally tapered end. When you shave, you remove the tapered portion, and the hair might be interpreted as growing back thicker than when it started growing of its own accord. Also, there might be a psychological aspect here, considering most people start shaving when their hair is thin and hormonal influences are changing growth patterns, leading to a bias where it might be seen that shaving could have been interpreted as a contributing factor in the thickening of hair.
This argument is often used to justify waxing over shaving. In comparison to waxing, shaving does result in a thicker distribution of hair. This is because the hair follicles are damaged over time with waxing, leading to fewer hairs growing and a less thick distribution of hair. There is no such reduction in number of hairs with shaving because the blade cuts at the surface of the skin and does not affect the follicles like waxing. Shaving itself does not cause hair to be thicker, but unlike waxing, it does not cause hair to be thinner and thus results in a comparatively thicker distribution of hair.
Shaving is one way of removing unwanted body hair. For some that can't take the pain of waxing, shaving is the easiest way. Shaving makes the body hair looks coarser and darker as it grows back, and many people believe that this is true when it is really not. As we look at the hair shaft diagram, we can see that the hair shaft decreases at the end that gives us soft and thin body hair. When you shave, you are cutting the midshaft of your body hair and because you've already cut the tapered end, what you'll see is the thicker part of the hair. It is not also true that shaving causes hair darkening. It only appears to be that way because it is more noticeable. So I'd say shaving doesn't cause hari thickening and darkening.