In that case, I would understand "quietly judging you" to mean that he is judging him for his own evaluation only. An evaluation that is not to be shared. I did not see the movie, but it sounds like it was a negative judgement.@pob14 Interesting. There's a scene in the movie Magnolia where Tom Cruise is being interviewed, and the interviewer asks him an awkward question.
He remains silent, and she says: "What are you doing?". He answers: "I'm quietly judging you".
I'm not sure if in that context, "quietly" is the same as "silently", or whether they use that adverb for emphasis purposes.