“Right as rain” means things are absolutely fine, perfectly correct, just the way they should be. For example, “He was very ill, but he’s right as rain now.”
The phrase originated in Britain, where rainy weather is a normal fact of life and was first recorded in 1894. Part of the reason for its popularity may be the alliteration.
However, since medieval times, there have been expressions beginning “right as…” and always in the sense of something being satisfactory, secure or comfortable. The oldest example I’ve seen is from the Romance of the Rose of 1400: “right as an adamant,” where an adamant was a lodestone or magnet.
In 1546, the synonym for “right as rain” was “right as a line,” probably assuming the line was straight and therefore desirable, or acceptable.
From 1837, in Charles Dickens’s Pickwick Papers, is found “right as a trivet” (a trivet being a stand for a hot dish): “ ‘I hope you are well, sir.’ ‘Right as a trivet, sir,’ replied Bob Sawyer.”
The Historical Thesaurus of the Oxford English Dictionary lists the phrase “all is gas and gaiters,” meaning “everything is fine.” That began with Charles Dickens’ 1839 novel Nicholas Nickleby. Dickens probably meant it as a nonsense phrase, but it caught on and became popular in 1800s Britain.
The first appearance of “right as rain” appears to be from Max Beerbohm’s book Yet Again, published in 1909: “He looked, as himself would undoubtedly have said, ‘fit as a fiddle,’ or ‘right as rain.’ His cheeks were rosy, his eyes sparkling.”
If English speakers had lived on the Wet Coast of British Columbia in medieval times, they would have come up with the “right as rain” phrase, too. Or perhaps, “gray as a November day.” It’s the price we pay for living in paradise.