Something that costs “an arm and a leg” is something that can be acquired only at great expense. The term “cost an arm and a leg” appears to have started in the United States immediately after World War II—when many soldiers returned home without arms and legs.
 
“The habit the good Saratoga burghers have of taking practically an arm and a leg the prices they charge visitors” was cited in a newspaper on September 3, 1946. “The Hawks (Chicago Blackhawks ice hockey team—ed.) will have to give an arm and a leg to acquire any respectable major league talent” was cited on December 3, 1946. On September 11, 1946, it was noted that an amputee magazine’s “subscription price is the most expensive of any publication in history—it costs an arm or a leg!”
 
The idiom to “cost an arm and a leg” is often combined with being waited on “hand and foot,” as in “Restaurants where they wait on you hand and foot are where they charge you an arm and a leg.”
 
   
Wiktionary: an arm and a leg
Etymology
The loss of an arm and a leg would be a high price to pay for something.
Noun
arm and a leg
1.(idiomatic) A very high price for an item or service; an exorbitant price; usually used after the verb cost. 
 
(Oxford English Dictionary)
an arm and a leg  n. colloq. an enormous amount of money, an exorbitant price; freq. in to cost an arm and a leg.
1956   ‘B. Holiday’ & W. Dufty Lady sings Blues xxiv. 224   Finally she found someone who sold her some stuff for an arm and a leg.
1979   Washington Post 6 Nov. b5/1,  I acquired good taste over the weekend. And it didn’t cost me an arm and a leg.
1992   World of Interiors July 14/3   How to use colour and smarten up the kitchen—hopefully all without spending an arm and a leg.
 
2 September 1946, The Times-Picayune (New Orleans, LA), pg. 8, col. 2:
$21,000,000 Meeting Assures
Continuance of Racing at Spa
(The Associated Press)
SARATOGA SPRINGS, N. Y., Sept. 1.—Reports of the death of the Saratoga track, it would appear, were greatly exaggerated.
(...)
The story was that the 15 per cent tax and track “bite”—16, counting breakage—from the mutual machines, and the competition of the New Jersey tracks—(Col. 3—ed.) they’re within two hours of New York while the spa is nearly five away—and the habit the good Saratoga burghers have of taking practically an arm and a leg the prices they charge visitors for all commodities would scare the customer away.
 
11 September 1946, Lima (OH) News, ‘These Boys Don’t Like The Word ‘Handicap’” by Kenneth L. Dixon (INS), pg. 8, col. 4:
For instance, their organization magazine carries the notation that its subscription price is the most expensive of any publication in history—it costs an arm or a leg!
(Cleveland’s Possibilities Unlimited, Inc., an amputee organization—ed.)
 
3 December 1946, Rockford (IL) Register-Republic,  “Hawks, So It’s Reported, Need Some Ice Skaters” by Charles Einstein (INS), pg. 13, col. 8:
The Hawks (Chicago Blackhawks ice hockey team—ed.) will have to give an arm and a leg to acquire any respectable major league talent, and the minor league picking, currently under examination by President Tobin, are reported to be on the slim side.
 
8 December 1949, Long Beach (CA) Independent, “Christmas Suggestions,” pg. 12-B, col. 5:
Also Food Editor Beulah Karney has more than 10 ideas for the homemaker who wants to say “Merry Christmas” and not have it cost her an arm and a leg.
 
31 October 1951, Boston (MA) Traveler, pg. 25, col. 5 ad:
It needn’t cost an arm and a leg for decorator service…not at ALPERT’S, where you’ll find the decorators very friendly and far from overbearing…
(...)
ALPERT’S FURNITURE
 
16 September 1956, New York (NY) Times,“TOUTING FOREIGN FILMS; Their Possibilities Are Commended To the Theatre Owners of America Expediency Dubious Items” by Bosley Crowther, pg. X1:
That is to say, there is a shortage of sure-fire money-malting films a theatre operator can latch on to without paying an arm and a leg.
 
20 January 1957, Boston (MA) Globe, “Horace Sutton’s Travels: The Eating Good in Belgium; And It’s Cheap, Too,” Vacation Section, pg. A4:
L’Epaule do Mouton means the sheep but at $14 for lunch for two, what it charges the tourist is an arm and a leg.
 
OCLC WorldCat record
Safety Training That Works—and Doesn’t Cost an Arm and a Leg
Author: Tita Beal
Edition/Format: Article
Publication: Training, 14, 8, 47,49-50, Aug 77
Database: ERIC The ERIC database is an initiative of the U.S. Department of Education.
Summary: A safety training program for line managers at the Du Pont Corporation is described by a training materials company president. The program is said to be more worker-oriented and cost-effective through training line managers to administer safety training programs to their subordinates instead of using safety staff specialists. (MF)
 
OCLC WorldCat record
An arm and a leg : the human and economic cost of unsafe products.
Author: Australian Consumers’ Association.
Publisher: [Marrickville, NSW] : Australian Consumers’ Association, [1989]
Edition/Format: Book : English
 
OCLC WorldCat record
Arm and a leg
Author: David Ralph Martin
Publisher: London : Heinemann, 1998.
Edition/Format: Book : Fiction : English