[Apparently the oldest memorial in the graveyard, predating the earliest known Walney parish register (1744). There are references in the register of the parent church at Dalton to George Case and his family of North Scale] [Source]

The Walney Registers 1744-1900 has the following:

Geo. Case of Northscale. Buried at Walney Chapel Nov. 18 1758. I assume that the 1748 identified
above is a transcription error. (Check)

Unfortunately I have been unable to find any detailed information regarding these George Cases.
Presumably they were quite wealthy, being able to afford the new fashion of having a gravestone.

Case is an old family name in Furness; there still being farmers of that name locally. RF Case produced beer at their Cavendish St site in Barrow from 1867 – 1972, though this may not be connected to the above grave, the brewery having first been established in Ulverston. [Source]

A family tree in the Archive & Records Office covering the period 1600 – 1900 has Cases living at Leece, ‘The Manor’, Roosebeck and Peasholme.