I know this is an old thread, but I just saw it for the first time yesterday. I have been a practicing physician for 24 years, and I have a son who is a senior in HS, to put my response into context. Before attending medical school, I received an MS degree in physical chemistry. I really enjoyed teaching, but, wasn’t cut out for the research part of a basic science. I have seen this issue from every side of the problem. When I was an undergrad in chemistry, for example, my professor effectively failed an entire class of graduate students because I made the highest grade in the class, and he didn’t think I “deserved” an A in his course. At the time, I was a junior in a flagship state university that is consistently ranked in the top 30 or so in the US for chemistry. His basic problem, and he told me to my face, was that he didn’t want me to graduate with a perfect 4.0 in undergrad, which I had going into his course. My overall grade was 92%. Obviously, I survived.
The course I taught as a teaching assistant was junior year physical chemistry lab. I was the head teaching assistant, so I supervised the other teaching assistants and frequently acted as a mediator between the students and the professor and other TAs. Like the OP, I acknowledged that most of the students were “average”. Of course, average in a third-year college chem course means something different than average in college algebra. I tried to be fair. When I presented the grades on all the experiments to the professor, I would always point out the average grade for teaching assistant A was 78% while that of teaching assistant B was 37%. The professor ultimately assigned the grade, of course. In this setting, there was usually consistency in performance of students in comparison to their peers, despite being graded by different TAs, and there were usually consistent cut points at the end of the term. I have observed the same over the years when I judge grade school science fairs. We might all give different grades, but, whoever comes out on top is consistent.
I can only conjecture on why one TA gives a mean grade of 37 while another gives a 78. However, I think it has more to do with the personality of the TA than the specific student.