I’m assuming a double skin wall consists of an inner and outer stone wall with the gap between them filled with packed earth. I have never gotten deep into the weeds on such matters, but my layman’s guess is that these might have been a common evolution. One would start with an earthen rampart, probably ditched, and perhaps with a wooden palisade (if in a wooded region) or light stone wall on top. A natural next step would be to add an outer face of stone to get a stronger and more nearly vertical wall on the business side. The inner stone facing would come last, to reduce erosion and stabilize the fighting platform along the top. Do you have a sense of how common such constructions were? Would there have been any added advantages to this method other than time and cost of construction? For example, is this a preferred building technique in earthquake prone territory?
It would go up fast, and would yield a wide area at the top on which defensive garrisons could operate. A single curtain-style wall would better suit a town more concerned about bandits and other freelance raiders, and about the movements of the local regime's own citizens, and during the day the control of wandering traders. A capital would require more ambitious defenses.