أخوIbn Fāris denies this is an independent root at all: he treats the hamza as a substitute … (root khw)

The lexicographers in chronological order, from al-Khalīl to Lane.

Al-Khalīl's Kitāb al-ʿAyn presents the full paradigm directly: أخ, dual أخوان, plurals إخوة and إخوان, the abstract nouns أخوة and إخاء ('brotherhood, fraternizing'), and the denominative verb آخيته, with the Ṭayyiʾ dialectal variant واخيته traced to a root وخي; he also registers the feminine أخت (tāʾ realized as hāʾ) and the homonymous noun الأخية, the peg to which an animal is tethered, with its own verb أخّيت/تأخيت. Ibn Fāris, writing after al-Khalīl, refuses hamza-khāʾ-wāw root-status altogether: he states the hamza here is a substitute for an original wāw and directs the reader to his chapter on wāw, folding both أخ and الآخية into that analysis. This is a notable case of a later lexicographer analytically dissolving a term the earlier tradition had already fully paradigmatized.

What the theorists of sound symbolism would say of these letters. Speculative by nature.

Al-Dabbāgh glosses wāw as 'the intertwined things in the human being — veins, fingers and the like,' an image that resonates suggestively with kinship as an intertwining of lines of descent; the Akbarian correspondence table assigns wāw to 'the determination of ranks, stations and waystations,' which likewise echoes brotherhood as a designated station between people. Khāʾ is glossed by al-Dabbāgh as conveying extreme length together with fineness — harder to connect to 'brother' without strain. No data is supplied for hamza. Mainstream historical linguistics treats such correspondences as suggestive at most, not as etymological evidence.

The two-letter nucleus (Ibn Fāris's own chapters) and the permutations of the letters (Ibn Jinnī).

No bi-radical nucleus data is supplied. Among the six triliteral permutations, Ibn Fāris's own testimony marks أخو itself as no true root (the hamza being a disguised wāw); of the remaining arrangements أوخ, خأو, وأخ, وخأ are unattested, and only خوا (khawiya, 'to be empty, to collapse') is registered as a genuine root elsewhere, with no evident sense-connection to kinship. This is offered as a bare juxtaposition, not an asserted derivation: two of the six arrangements of these letters are alive in the language, and only one is fully paradigmatized, even though its own lexicographer disowns its root-status.

Cognates in the sister languages, and whether the word was borrowed.

ʾAkh is one of the most stable nouns in Semitic: Hebrew ʾāḥ, Aramaic/Syriac ʾaḥ(ā), Akkadian aḫu, and Geʿez ʾəxw all continue a common Proto-Semitic *ʾaḫw- 'brother.' The Arabic feminine أخت similarly matches Hebrew ʾāḥōṯ and Aramaic aḥāṯā. Given this depth and breadth of attestation, ʾakh is certainly an inherited Proto-Semitic kinship term, not a loanword from any sister language.

How the classical exegetes read the word in the Quran.

Al-Ṭabarī and al-Rāzī read أخ across the Qurʾān in both its literal legal sense — siblings in the inheritance verses 4:11–12, where distinctions of full, paternal, and uterine brothers matter for the fixed shares — and its extended sense of religious fraternity, believers addressed as brothers to one another. In 2:178, on retaliation, 'his brother' (akhīhi) is read as the victim's next of kin or the wronged party generally, who may accept blood-money instead of retaliation. Al-Rāghib notes the semantic stretch from blood-kinship to any bond of close association or shared cause, which underlies the Qurʾān's use of akh for spiritual or tribal solidarity as well as literal siblinghood.