"The visits to Harvard from these three prominent landscape planners provided a survey of the state of the art to the group that emerged from the Laboratory" -Nick Chrisman, Charting the Unknown (page 43)
GIS undoubtedly has its origins in the concept of the overlay.
Precisely who invented the overlay technique first or used it most effectively is debatable.
Attributing this technique to any one individual would be both fruitless and misleading.
Techniques were shared at the Harvard Graphics Laboratory in 1967, with visits from Angus Hills, Philip Lewis, and Ian McHarg (Chrisman, 2006, page 42).
Hills was associated with Tomlinson's Canada GIS and the Canada Land Inventory, but as Chrisman (2006, page 42) notes, "Hills's was the [technique] that needed GIS the least" because "each of the CGIS layers depended on expert photointerpretation."
Lewis (from the University of Wisconsin) used transparent map overlays to explore environmental corridors.
McHarg was famous for using comprehensive datasets cumulatively to delineate areas of constraint/possibility in the theory and practice of design with nature.
Design With Nature is classic of early or proto-GIS thinking. I checked out McHarg's book from Bedford Library just to have a look at it again.
Snow used overlays as well, a good century or more before McHarg. You can check out the classic text on cholera, On the Mode of Communication of Cholera, on Google Books.
This post is an overlay of converging possibilities that fed into what is emerging in recent decades as a very plural universe of GIS possibility.
Chrisman, Nick. 2006. Charting the Unknown: How Computer Mapping at Harvard Became GIS. Redlands: ESRI Press.