Re: Burden B/Audrey C
Expressions starting right as have been around since medieval times, always in the sense of something being satisfactory, safe, secure or comfortable. An early example, quoted as a proverb as long ago as 1546, is right as a line. In that, right might have had a literal sense of straightness, something desirable in a line, but it also clearly has a figurative sense of being correct or acceptable.
Right as rain is actually a fairly recent addition to the simile, early 20th century. The first time it showed up was in writing. It was from Max Beerbohm’s book Yet Again of 1909: “He looked, as himself would undoubtedly have said, ‘fit as a fiddle,’ or ‘right as rain.’ His cheeks were rosy, his eyes sparkling.”
I guess the idea is that rain often comes straight down, in a right line, to use the old sense.