It goes back much further than the late 18th century. This is a decent summary, although a bit short on citations for my liking:

https://thecontractsguy.net/2014/02/02/spacing-after-periods...

   Literally centuries of typesetters and 
   printers believed that a wider space was 
   necessary after a period, particularly 
   in the English-speaking world.  It was 
   the standard since at least the time 
   that William Caslon created the first 
   English typeface in the early 1700s (and 
   part of a tradition that went back further),
   and it was not seriously questioned among 
   English or American typesetters until the 
   1920s or so.

Extra space after each sentence was and is a good idea, whether you're talking about handwritten documents or typeset ones. Typewritten documents arguably benefit the least from the practice. Point being, when single-space advocates say that double-spacing is obsolete and unnecessary because we don't use typewriters anymore, they are just plain wrong.