What's the etymology of las tantas in the meaning of very very late?
loc. sust. f. pl. coloq. Una hora muy avanzada del día o de la noche.
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Probably from "a las tantas" an abbreviation of "a las tantas horas" in this case.
This form is used to express when something is happening or happened at an unknown/unexpected late date or time and can be literally translated as "at such hours" or "at the many",
Spanish: a las tantas horas de la mañana llegó
English: at such/so many hours in the morning he arrived
I can't say there's an etymology related to the use, as this is used for the fact that the hours are counted and the more you get (las tantas), the later it is.