How did Semitic languages fit biliteral roots into triliteral paradigms?

[Ahzoh]

I've been reading around regarding the evolution of Semitic roots, for the sake of my own project.

It seems to be the case that there were a lot more "biliteral roots" in Semitic languages (or Proto-Semitic or Pre-Proto-Semitic) before the advent of agriculture and after agriculture the number and frequency of triliteral roots increased (and possibly replaced biliteral roots) as suggested by this article

It's also suggested by papers I've read that some or many triliteral roots are derived from biliteral roots that were augmented by an affix, although it is either argued by other papers that it's merely coincidence or it was very very limited and that most triliteral roots are in fact underived and simply supplanted the biliteral roots. Relating to all that there is this article

From the PLOS ONE article I linked and some other paper I've read, I believe it to be the case that:
a) biliteral roots with a short vowel reduplicated the second consonant (e.g. dan > danan) or did full reduplication (e.g. dan > dandin)
b) biliteral roots ending in a vowel, short or long, tend to be augmented with a glide (e.g. qalu > qalaw)

Also according to this a biliteral root may be augmented by a prefix such as n(a)- (e.g. Akk. našāqu(m) "to kiss") and w(a)- (e.g. Akk. wabālu(m) "to carry")

And the w-initial roots do have strange behaviour in the paradigms of Arabic with some of them eliding the w in the nonpast stems (e.g. wajad-a "find" > ya-jid-u) while rarely others keep them (e.g. wajil-a "to be scared" > ya-wjal-u).

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Given all that, there are still things I cannot find out about:

1) The origin of hollow (middle-weak) roots. I suspect they come from biliteral roots with a long vowel or diphthong, but I'm not sure.
2) The origin of intitial-weak roots
3) the meaning imparted by the n- and w- augments, if any. I did read that sometimes the w-initial radical was found in a lot of stative verbs

[bradrn]

I don’t know about the detailed diachronics, but to answer the title question: not all of them did. Plenty of Semitic languages retain separate paradigms for the remaining biliteral roots.

[Arzena]

And the w-initial roots do have strange behaviour in the paradigms of Arabic with some of them eliding the w in the nonpast stems (e.g. wajad-a "find" > ya-jid-u) while rarely others keep them (e.g. wajil-a "to be scared" > ya-wjal-u).

To that end, the imperative form of Arabic verbs beginning in /w/ - like wasala 'to arrive' - drop the /w/ too: sil 'arrive.IMP.sg.masc'. Yet, as you progress a verb through the Forms, an initial /w/ will be maintained - eg., Form 2 wassala/yuwassilu, Form 4 awrada 'transport' from Form 1 warada 'come, arrive' cf. Form 10 istawrada 'import'. - but in Form 8 it assimilates into a germinated /tt/, eg., ittasala 'communicate' from Form 1 wasala. This phenomenon could reflect he fossilization of /w/ becoming analyzed as part of the root, an evolution from its earlier function as a mere particle, hinted at the dropping of /w/ from Form 1 nonperfective and imperatives verb forms.

By contrast, however, the modern spoken Arabic languages tend to preserve the /w/ by analogy with the structure of Form II verbs (which in Modern Standard Arabic produces a transitive or causative meaning): eg., Form I wasala/yasal 'arrive'; Form II wassala/yuwassilu 'bring together' but Egyptian Arabic wasal 'arrive', present indicative yiwasal.

I wonder if the /w/ elision in Arabic AND the occurrence in Hebrew of initial /y/ for /w/ in cognates with Arabic - cf. walad 'boy' and yeled 'id' - reflects an original Proto-Semitic root */lada/ with Arabic having the particle *wa 'and' fused to the root and the Hebrew /y/ reflecting the third person masculine verbal conjugation becoming perceived as part of the root.

[bradrn]

I wonder if the /w/ elision in Arabic AND the occurrence in Hebrew of initial /y/ for /w/ in cognates with Arabic - cf. walad 'boy' and yeled 'id'

My understanding is that the latter is an old and well-attested sound change /w/→/y/ in NW Semitic . I don’t know anything about Arabic /w/-elision, but I doubt that it’s connected.

[Arzena]

I've read that, too, and it's definitely more sound than my speculation. Let's hop in the time machine to find out