These are some notes on the Greek word εὐσέβεια (eusebeia), and its roots εὐ- (eu-) and σέβομαι (sebomai).
See William Barclay’s “New Testament Words” for a comprehensive summary of history and references in classical Greek, and in the New Testament.
Origin and history: Chantaine’s Etymological Dictionary
In entry for sebomai and variants:
La diversité remarquable des emplois se réduit à la signification unique «se retirer», ou «faire se retirer» confirmée par l’étymologie, cf. [Sanskrit]. tydjáti «quitter, abandonner» de *tyegω-, avec tydjas-, tyaktdr-, tyaktá- que l’on n’a pas le droit pourtant de rapprocher de σέβας, σέπτωρ, σεπτός (formations parallèles). Doutes injustifiés de Mayrhofer, Elym. Wb. des Allind. 1,529. Voir encore Pokorny 1086.
The remarkable diversity of uses reduces to the single meaning “withdraw” or “to cause to withdraw”, confirmed by the etymology, cf. [Sanskit] tydjáti “leave, abandon” of *tyegω-, with tydjas-, tyaktdr-, tyaktá- which, however, should not be linked with σέβας, σέπτωρ, σεπτός (parallel forms). Unjustified doubts of Mayrhofer, Elym. Wb. des Allind. 1,529. Also see Pokorny 1086 — (translation by me, DeepL).
In: Pierre Chantraine (1968) Dictionnaire étymologique de la langue grecque: histoire des mots, Klincksieck, Paris, p 993. Archive.org
Beekes, Etymological Dictionary of Greek
σέβομαι [v.] ‘to shy, feel ashamed’ (Δ 242), post-Hom. ‘to be in awe, honor, worship’, especially with regard to the gods. [origin is] Indo-European *tieg’- ‘leave alone, give up’.
In Robert Beekes (2010) Etymological Dictionary of Greek, Brill, Leiden, p 1315. Archive org
Use of sebomai in the Iliad
The Iliad may have been written around 522 BC, and so reflects early (archaic) Greek usage.
In the Iliad, the author uses sebomai with the meaning of shame:
’Αργεῖοι ἰόµωροι, ἐλεγχέες, οὔ νυ σέβεσθε; (Argives, arrow-fighters, do you have no shame, you worthless men? Il. 4.242) — source, also Homer, Iliad, 4.
Plato’s Definitions
From around 300 BC:
εὐσέβεια (eusebeia), piety: justice concerning the gods; the ability to serve the gods voluntarily; the correct conception of the honor due to gods; knowledge of the honor due to gods.
In Douglas S. Hutchinson (translator). Definitions*. In John M. Cooper (ed.): Plato. Complete Works, Hackett Publishing, Indianapolis/Cambridge 1997, ISBN 978-0872203495, pp. 1677–1686).
Plato and eusebia “to gods and to parents”
Eusebia can also apply to persons deserving of reverence.
Plato’s Republic 615c (around 375 BC):
εἰς δὲ θεοὺς ἀσεβείας καὶ εὐσεβείας καὶ τε γονέας καὶ αὐτόχειρας φόνου μείζους ἔτι τοὺς μισθοὺς διηγεῖτο.
Plato’s Republic, translation by Benjamin Jowett:
Of piety and impiety to gods and parents, and of murderers, there were retributions other and greater far which he described.
Nero and eusebia as due-reverence to a person
A 67 AD inscription containing a proclamation by Nero:
Since I wish to reward most noble Greece for its good will and piety [eusebeia] towards me, I order that as many as possible from this province attend at Corinth on November 29th.
This usage is roughly contemporary with the writing of e.g. 1 Timothy.