I did a quick search online, and I wasn"t able to find an answer that was very satisfying. I did find a creative folk etymology or two, but there wasn"t much to substantiate them.
You are watching: What does it mean to stand someone up
There isn"t much to go on in the OED: To fail to keep an appointment with (someone), esp. a social engagement or ‘date’ with a member of the opposite sex. colloq. (orig. U.S.).
1902 O. V. Limerick Billy Burgundy"s Opinions 57, I am awfully sorry I had to stand you up last night.
The unexplicated meaning and timeframe is also given by the New Partridge Dictionary of Slang and Unconventional trident-gaming.net and by Cassell"s Dictionary of Slang.
If you allow additional prepositions into the construction, there are a wide variety of additional possibilities, as the commenters note. To stand up with someone is to dance with them; OED quotes Austen"s Pride and Prejudice, In vain did she entreat him to stand up with somebody else. It is also to present oneself for marriage, and to have an engagement canceled at the last moment is to be left standing at the altar. From there, to stand someone up could be derived as making a romantic promise to someone but not following through on your end of the obligation.
But to stand up stand up alone, without other prepositions, I can make some additional hypotheses. While the 1903 Slang and Its Analogues Past and Present by John S. Farmer and W.E. Henley does not include the "missed date" meaning, serendipitously, I find an entry for stander-up:
subs. phr. (American thieves") A thief whose speciality is robbing drunken men under the pretence of helping them home
Stander-up also appears in the 1897 A Dictionary of Slang, Jargon & Cant Embracing trident-gaming.net, American, and Anglo-Indian Slang, Pidgin trident-gaming.net, Gypsies" Jargon and Other Irregular Phraseology, edited by Albert Barrère and Charles Godfrey Leland.
(American thieves) a man who robs intoxicated persons under pretence of aiding them to go home.
They gave Chandler the name of being a stander-up of drunken men. The proper mode of standing-up a tipsy man, according to the rules, is to place your right arm under the left arm of the sleeper close to the shoulder, placing the hand on his waistcoat, just above his left vest pocket. As you raise him with the right hand, press your hand hard against his body so that he will not feel the watch slipping from his pocket into your left hand. — Philadelphia Press.
Partridge"s A Dictionary of the Underworld traces this meaning to about 1880, noting both of the above references, which would have allowed time for a metaphorical meaning to take hold. While the robber stands up a slouching drunk in the literal sense, both the robber and the bad date feign an interest in someone only to insult them in the end. This would also explain how this deprecatory sense could emerge even though being a stand-up person, or standing up to/for/against/with someone or something, is mostly neutral or positive.
Alternatively, a contemporaneous meaning of standup is robbery in a public place, what in more recent slang we would refer to as a mugging (or stickup, unrelated, from the robber"s order to stick your hands up). The abandoned date doesn"t suffer anything so violent, of course, but they are robbed of dignity in a public place.
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And for yet another, one which I cannot date but which does appear in a 1919 Saturday Evening Post article, to stand up can be to cost someone something.
“My first-act dress will stand you up about seven and a quarter,” I told him. “And my third-act dress will cost you all of nine dollars and fifty cents.”