What is the origin of "right as rain"?

I looked this up, and came up with:.

It makes no more sense than the variants it has usurped and is clearly just a play on words (though perhaps there’s a lurking idea that rain often comes straight down, in a right line, to use the old sense).

The author here doesn't seem to know very clearly what its origin is. He is speculating it's just a play on words.

Does anyone have any definitive answer or evidence?

Your source World Wide Words makes the point that the phrase right as... has appeared in many forms over the years and that right as rain probably became the favoured variant because of its pleasing alliteration. It seems like a reasonable conclusion and all I can do here is add further support to his theory from an earlier example.

This is from In the Midst of Alarms by Robert Barr, 1894:

"To whom are you engaged? As I understand your talk, it is to Miss Bartlett. Am I right?"

"Right as rain, Renny."

Perhaps it was a phrase that was already in common usage at this point but the triple alliteration here is striking.

Meaning

The Godzone Dictionary: Of Favourite New Zealand Words and Phrases (2006) says:

The expression right as something has been used in English since medieval times, using a string of comparatives, such as trivet or ninepence. Right as rain emerged in the 19th century and took precedence over all the other forms, possibly because of its pleasing alliteration, and also possibly because rain is perceived as good, and causes growth.

But a book review of the 1955 Dictionary of Early English by Joseph T. Shipley in the June-July 1956 edition of The Crisis magazine says:

Few of us are aware that many commonly used words once had meanings, in many cases, quite the opposite as those now current. Right, in the phrase "as right as rain," originally meant straight in direction.

And The Wordsworth Dictionary of Idioms (1993) agrees. It says as right as rain is:

A pun on the original meaning of right = straight.

The Free Dictionary gives these meanings of right:

adj.
11. Straight; uncurved; direct: a right line.

adv.
2. In a straight line; directly: went right to school.

The American Heritage Dictionary of Idioms (1997) says:

In good order or good health, satisfactory, as in He was very ill, but he's right as rain now, or If she'd only worked on it another week everything would have been as right as rain. The allusion in this simile is unclear, but it originated in Britain, where rainy weather is a normal fact of life, and indeed W.L. Phelps wrote, "The expression 'right as rain' must have been invented by an Englishman." It was first recorded in 1894.

Antedatings

The OED's first quotation is:

1891 G. Parker in Good Words May 330 ‘Right as rain,’ said the engineers.

It appears in an earlier dictionary, A dictionary of slang, jargon & cant embracing English, American, and Anglo-Indian slang, pidgin English, tinker's jargon and other irregular phraseology (1890), by Albert Barrère:

Right as rain (popular), quite right, safe, comfortable.

There was six of us took the rattler at King's Cross by the first train in the morning, and we'd got three briefs and a old 'un with the date sucked off— right as rain we was ! We got a kerridge all to ourselves, nice and comfortable. — Sporting Times.

The earliest I found is in Hence these tears (1872) by J.B.L. Warren (read online):

" ... Is all quiet outside"? "Right as rain," replied Christopher, pushing his head beyond the door to listen.

It was also used in the 1870s in Australia and New Zealand. The earliest in the Australian Trove newspaper archive is from The Gundagai Times (Friday 25 August 1876 p2 Article):

this thoroughly practical farmer tells us he has a crop of oats ten or eleven inches high, looking as "right as rain," and he attributes this result entirely to the fact of steeping and manuring the seed, thus getting a start of the
weeds.

And from New Zealand's Papers Past archive is the Akaroa Mail and Banks Peninsula Advertiser (28 January 1879, "The Sundowners Swag"):

I thought when the Bank business was played out that Knickers would be dead broke, but no, he is still to the fore, and "right as rain," for I heard him the other day stave off a long-suffering creditor by telling him "that that confounded Afghan war was the cause of his remittance not coming by the last mail."