This paper is '98 and it contrasts the then prevailing theories, in contrast with dialectal and historical evidence, arguing that the origin of periphrastic "do" was a habitual aspect marker.

Two of the earlier hypotheses that the author addresses and criticise:

Contact with Celtic languages - the feature would be borrowed from other languages that English interacted with. Specially prominent due to distribution, as do-periphrasis appeared first on the Western dialects. However unlikely, given that Celtic substratum influence in English was relatively minor.

Some invoke more complex pathways, such as a potential early Germanic-Celtic creolisation; the author claims that this is unattested.

Causative 'do' - occasionally attested in Old English, and frequently in Middle English. I'll adapt the 5a example to highlight the construction:

• I do to-you know[=witan]... that those devil-idols to-you are harm-bearing

Here the usage of "do" would initially mean something like "make", "cause to", "have". For another example [from my own], consider "I did her tell me what was going on" - the "do" has some meaning but it's rather messy, and dependent on the sentence. (Does that "did" mean "encouraged?" "forced?" "asked?")

The author sees the following problems with this hypothesis:

• Origin - do-periphrasis originated in the Western dialects, but those were the one that used causative do the least.
• Motivation - it's harder to claim that an optional causative "do", with no independent semantic value, would eventually evolve into the do-support currently used.

Other hypotheses addressed were the usage of 'do' as a perfective aspect marker and verbal ellipsis. And then the author actually addresses the hypothesis he believes to be correct, linking current do-support to the habitual aspect; for example, in the sentence "I do browse Lemmy", that "do" can be understood as both an emphasiser and as conveying "by rule, usually".