“Everybody invited and nobody slighted!” is the old-time invitation to a country dance. The phrase’s origin is unknown, but it’s been in use since at least the 1920s.
 
 
14 July 1923, Atlanta (GA) Constitution:
Notice—Stop, look and listen, there is going to be a party at Mr. and Mrs. Clyde Houck’s Wednesday night, everybody invited, nobody slighted, so everybody remember it and come.
 
7 October 1926, Ada (OK) Weekly News, pg. 6, col. 1:
There will be preaching Saturday night, Sunday and Sunday night. Everybody invited, nobody slighted.
     
Google Books
Coffee in the Gourd
edited by J. Frank Dobie
Austin, TX: Texas Folk-Lore Society
1935
Pg. 31:
These men made a tour of the country and invited every person they happened to meet, regardless of who it might be. The invitation usually contained the phrase, “Everybody invited and nobody slighted.”
 
Google Books
Texas Folk and Folklore
compiled by Mody Coggin Boatright
Dallas: Southern Methodist University Press
1954
Pg. viii:
We believe that this book ought to be as much fun as an old-time cowboy dance. Like the cowboy who rode about carrying the news of the dance, we say to you, “Everybody invited and nobody slighted!”
   
25 July 1971, Dallas (TX) Morning News, section A, pg. 12:
“The hosts for a Texas Josey party would spread the word formally—everybody invited and nobody slighted, the phrase went,” Abernethy explains.