The phrase here’s looking at you is used as a toast in drinking.

It is now widely associated with the American film Casablanca (1942), directed by Michael Curtiz¹, in which Rick Blaine² addresses Ilsa Lund³ with the words:

“Here’s looking at you, kid.”

¹ the Hungarian-born American film director Manó Kaminer (1886-1962)
² played by the American actor Humphrey DeForest Bogart (1899-1957)
³ played by the Swedish actress Ingrid Bergman (1915-82)

The earliest instance of here’s looking at you that I have found is from The New York Herald (New York City, N.Y.) of 12^th March 1871, in a dialogue between a Herald reporter and Bill, a duck hunter who builds boats specially designed for his activity:

Hunter—“Come in the carpenter shop; I’ve got a few boats stowed away. Mebbe you’d like to look at one for yourself.”
[…] My ruminations were brought to an abrupt close by a request to “Join in a social nip, Cap. You see, I keep old ‘tear-heel’ on hand; the ‘boys’ come down to see me once in a while and I have to use them well.”
Reporter—“Here’s looking at you.” I tried to swallow it, but it was “tear throat,” instead of tear heel, and I was forced to desist. Bill was too intent on getting away with his “nip” to notice me. I took advantage of his rapture, and threw the stuff behind me, and just got the empty glass back to my lips when Bill, having got back to earth once more, asked me how I liked it.
“Like it,” said I, with tears in my eyes, “its [sic] the only real stuff I have tasted this many a day.”

The phrase here’s looking toward you has been similarly used; for example, on 13^th April 1893, The Buffalo Commercial (Buffalo, N.Y.) published an article about Russian hospitality, which contains this paragraph:

Capt. Besobrassof was so good as to order glasses of chartreuse and benedictine, and all took their choice of these liquors. The captain waited till every lady had her glass in her dainty fingers, and then proposed the Russian toast. “Vosh us durrivia.” It means the same as “A votre sante” in French, “Gutheil” in German, and “There’s your good health” in English. It also means the same as “How” in our army and “Here’s looking toward you, old pard” in the mining camps of California.

I have found an early occurrence of here’s looking at you, kid that perhaps does not allude to Casablanca; it is from the last line of April Nightmare, a poem published in the Barnard Bulletin (New York City, N.Y.) of 1^st April 1943:

And then we awoke. It was just April First.
p.s. Here’s looking at you, kid. Happy A. First.

Alba Rufe placed the phrase from Casablanca in a historical context in ‘Cheers!’ They Chorused With Glasses Raised on High, published in The Morning Call (Allentown, Pennsylvania) on 28^th December 1963:

When Humphrey Bogart stared calculatingly at his leading lady and raised a glass to lips in some forsaken Paris bistro, he’d say quietly:
“Here’s looking at you, kid.”
When a western hero’s sourdough sidekick hefted a slug of Red Eye in the Silver Dollar Saloon, he’d bellow:
“H’yars mud in yer eye!”
For centuries people have been prefacing the first swig of nearly anything in a glass with some witticism or expression of good cheer.
Where the patter and glass-clinking started is anybody’s guess, but if it had a barbaric origin, it probably was a sort of farewell before a night under the table.
The relatively staid Englishman of the 16^th Century rarely drank himself into insensibility—if he were a gentleman, that is. It was in his time, though, that the term “toast” came about.
During the latter part of the Middle Ages it became the fashion in England to add toasted bread to drinks—not unlike the present-day custom of sogging doughnuts in coffee or pretzels in beer froth.
The Englishmen of the 16^th Century somehow related the mixing of toast and drink with fellowship and good cheer—perhaps like a communion—and, from this, the “toast” became a drink of honor, often applied to some fluttery young object of a gentleman’s affections.
That’s how the term “toast of the town” came about—in the 18^th and 19^th centuries. It applied, and still does, to a gal of far-reaching charm whose beauty and wit may been [sic] enough to drive a rejected suitor to drink.
Anyway, Richard Brinsley Sheridan⁴ coined one of the all-time classic toasts for his play “School for Scandal.” Quoth Sheridan:
“Here’s to the maiden of bashful fifteen.”
When the glasses of America come together this New Year’s eve, the most popular of toasts will be the traditional British “Cheers!” or the popular Scandinavian “Skoal!” or the old American standby “Bottoms-up!”

⁴ the Irish playwright Richard Brinsley Sheridan (1751-1816)—cf. picnic, to steal someone’s thunder, Yorkshire tyke, the theatrical origin of ‘claptrap’ and “the very pineapple of politeness” and other malapropisms