Schweppes is a brand of beverages; a jocular verb is “Schwepped” (which sounds like “swept”). “Schwepped her off her feet” was written in the story “Schweppes’ Chief Visits Pittsburgh” that was published in the Pittsburgh (PA) Post-Gazette on June 5, 1956.
 
The Saturday Review published this on August 28, 1965:
   
“I met a girl at a bar. She sat on the very next seat.
I bought her gins and tonic, and schwepped her off her feet. —WILL CONWAY.”
 
“A girl agreed to go out with me after I gave her a bottle of tonic water. Schwepped her off her feet” was posted on Twitter by Lord Kiel‏ on November 19, 2015.
 
     
Wikipedia: Schweppes
Schweppes (/ʃwɛps/) is a beverage brand that is sold around the world. It includes a variety of lemonade, carbonated waters and ginger ales.
         
5 June 1956, Pittsburgh (PA) Post-Gazette, “Schweppes’ Chief Visits Pittsburgh” by Vince Johnson, pg. 13, col. 2:
In 1940 he married a British girl after a romance that practically Schwepped her off her feet.
   
UNZ.org
Google Books
28 August 1965, Saturday Review, “The Phoenix Nest” edited by Martin Levin, pg. 8, col. 3:
Boy Treats Girl
I met a girl at a bar. She sat on the very next seat.
I bought her gins and tonic, and schwepped her off her feet. —WILL CONWAY.
 
Twitter 
Mr_Rixter‏
@MrRixter
Went to a club last night and bought a girl a lemonade .........schwepped her off her feet!
5:02 AM - 22 Sep 2010
   
Twitter
WAY UP‏
@ScottKerrWayUp
Replying to @Dittomusic
@Dittomusic just got this girl home from the pub, i schwepped her off her feet
9:26 AM - 27 Sep 2010
   
Twitter
Juan Arroyo‏
@JuanJArroyo4
Just been on a date. Bought her a lemonade. Schwepped her off her feet
6:42 PM - 16 Aug 2011
   
Twitter
Ashley Bayes‏
@ash82bunz
Threw a bottle of tonic water at my girl friend. Schwepped her off her feet.
4:57 AM - 1 Jan 2012
   
Twitter
Lord Kiel‏
@kiel_phillips
A girl agreed to go out with me after I gave her a bottle of tonic water.
Schwepped her off her feet.
#1PUN
7:00 AM - 19 Nov 2015 from Londonderry, Northern Ireland
   
Twitter
Shit Jokes‏
@ShitJokes
A girl agreed to go out with me after I gave her a bottle of tonic water.
Schwepped her off her feet.
2:40 AM - 20 Nov 2015
 
Reddit—Jokes
A girl agreed to go on a date with me after I gave her a bottle of tonic water.
submitted October 30, 2016 by WCatto
I schwepped her off her feet.
COMMENTS
[deleted]
I have no date… It’s Soda-pressing
 
Twitter
Shit Jokes‏
@ShitJokes
A girl agreed to go out with me after I gave her a bottle of tonic water.
Schwepped her off her feet.
11:07 AM - 10 Jan 2018