For "arrêtez", why isn't this "arrêtez-vous"? I have a feeling the "you" is implied, but for other sentences that give an authoritative order, "-toi" or "-vous" is added in front of the verb (like "Asseyez-vous sur cette chaise!" meaning "Sit down on this chair!"), so why not in this case?
For discussion on arrêter in particular, refer to Reflexive form of "arrêter" for habits
In your example of Asseyez-vous, vous is necessary because the imperative here is derived from s'asseoir, a reflexive verb, and a reflexive pronoun must be retained. (In the case of tu, it is changed to toi in certain situations.)
In general, however, it is not true that clauses that "give an authoritative order" (i.e. that are in the imperative) necessarily have a reflexive pronoun attached to the verb. If the verb in the imperative form is not reflexive, there will be no reflexive pronoun. (This may be more obvious if you rewrite these imperative clauses as declarative clauses.) For example:
Sauvez-moi de la mort qui m'attend ! (Save me from the death that awaits me!) Here, sauver is not used reflexively, and the clause is essentially the imperative form of Vous me sauvez …
Épargnez votre enfant ! (Spare your child!) Again, here, épargner is not used reflexively, and the clause is the imperative form of Vous épargnez votre enfant.
There are two forms of the verb to take into account, the transitive (arrêter qqc) and the pronominal (s'arrêter). Both can be constructed with a completing infinitive introduced by "de" (ref.1, ref.2, ref.3).
You can see from those ngrams that the two forms exist for the following verbs: "travailler", "fumer", boire". The meaning is the same. However, usage has it that you don't say "Arrêtez-vous de fumer." (at least not much, if at all) and only "Arrêtez de fumer is found." (ref.4). Similarly, for "manger" only the transitive form is used ("Arrête de manger.",
Arrête-toi de manger.", (ref.5)). Neither "Arrêtez-vous de manger." nor "Arrêtez de manger." are found and in the latter case this is understandable as le lack of familarity with the persons talked to proscribes formal injonctions; however "Arrêtez de manger." is correct.
When you are dealing with the verb "asseoir" or rather "s'asseoir" in the context you mention the big difference is that you don't have a choice, there is just one form, "s'asseoir".