Probably from basis (through the notion of a foundation of power); a sovereign (abstractly, relatively, or figuratively) -- king.
see GREEK basis
βασιλέα (basilea) − 15 Occurrences
βασιλεῖ (basilei) − 6 Occurrences
βασιλεῖς (basileis) − 16 Occurrences
βασιλεῦ (basileu) − 9 Occurrences
βασιλεὺς (basileus) − 48 Occurrences
βασιλεῦσιν (basileusin) − 1 Occurrence
βασιλέων (basileōn) − 11 Occurrences
βασιλέως (basileōs) − 9 Occurrences