Beside/besides seems to fall into the same grammar error category as toward/towards, forward/forwards, and backward/backwards. Many people aren’t sure when to the one with the -s.
Beside means by the side of or next to. He sat in the empty seat beside her. She moved the chair beside the window. That’s beside the point. (Here, it’s beside, not besides. In the idiomatic expression, beside means by the side of, that is, not directly on or not directly relevant to, as in not directly relevant to the point. It does NOT mean That’s in addition to the point.)
Besides means in addition to as a preposition and moreover as an adverb. Besides Weather Whys, Paul has written Literally, the Best Language Book Ever. Besides, I can’t go out on a school night.