On holiday in Algeria, I've been going frequently to some coastal rocks called əṣ-Ṣṭuħ الصطوح, from the plural of ṣṭəħ صطح "flat terrace roof", and occasionally eating šṭiṭħa شطيطحة "stew". I haven't done any dancing (šṭiħ شطيح) - not really my thing. But if I go into the mountains where they speak Kabyle, I might hear someone call something aməšṭuħ (amecṭuḥ) "small"; if they ask me whether I understand, I might reply šiṭṭuħ kan (ciṭuḥ kan) "just a little."
Can all these words be connected to one another? I think they might be.
Let's start with the easiest one: ṣṭəħ is obviously from Classical Arabic saṭħ سطح "flat roof, surface", a noun corresponding to the verb saṭaħa "spread out and level out". The root has cognates elsewhere in Semitic, notably Aramaic šṭaħ ܫܛܥ "to spread something flat" and Hebrew šāṭaħ שָׁטַח "to spread, stretch", so its Semitic origin is secure. (In the usual weird quasi-biradical way, it also fits into a wider pattern of "spread" words in s-ṭ, notably Arabic basaṭa "spread out".)
However, one notes that the sibilant elsewhere in West Semitic is, regularly, š. Could the various words with šṭħ somehow reflect an early parallel borrowing from Aramaic?
Let's start with Arabic: a verb šaṭaħa can indeed be found in Classical Arabic lexicons, meaning "to go too far". In Egyptian Arabic, Hinds and Badawi give šaṭaħ as "to veer, go off course". For Levantine Arabic, Neishtadt summarises a variety of sources as giving the range of meanings "to extend, lie down; to fell, slip (on the ground); to make a big step; to move away, depart; to go out, go for a walk, have a picnic, wander", while making the point that the verb must derive from Aramaic there.
A semantic link between "go far" and "spread out flat" is easy enough to envision: to be spread out flat is to be spread across the widest area possible. (Cf. English "stretch".) A priori, the easiest way to get from "go far" to "dance" is probably via the attested Levantine sense "to make a big step".
If Arabic šṭħ comes from Aramaic, then at some point one would expect it to have retained the original sense "to spread something out flat"; attested Levantine "extend" seems sufficiently close to this. Mašṭūħ would then be the past passive participle "spread out flat". Anything in such a state has been reduced to its minimum height; it would therefore be reasonable to call something particularly short məšṭuħ, or with the Berber nominal prefix a-məšṭuħ. From "short" to "small" to "little" seems sufficiently plausible.
The biggest remaining problem, then, is šṭiṭħa - are we to exclude this delicious dish from the lexical family? (Any direct derivation from "dance" is surely to be excluded, Wikipedia's fanciful proposal notwithstanding.) Neishtadt cites a suggestive Levantine form: šṭīḥ "flat plate usually made of sheepskin (which is used to cover the bread when kneaded / on which one puts the dough and then cuts it into small pieces)". Compare likewise Iraqi šaṭiħ "flat, shallow", used among other things to describe dishes. A plausible starting hypothesis, then, is that šṭiṭħa originally described the flat-bottomed pan in which the stew was prepared. The word has the form of a regular diminutive from a noun *šəṭṭVħ-a, which might be worth hunting for.
So, on a preliminary check, I'm inclined to say that yes: all the words discussed in the first paragraph derive from the same Semitic origin, one via Arabic proper, the rest via early borrowing from Aramaic. It's quite possible that wider lexicographic research would make it possible to fill in the missing steps in the semantic shifts directly, rather than speculatively - or that it would just complicate the picture further.
Addendum: Another member of this word family in Darja is ṭəħṭaħa طحطاحة "flat expanse (of land)". Good luck simultaneously reconciling both that and basaṭa with a biradical analysis.