1) A late alternative of ‘sty’ which may have developed when the meaning of that word was no longer transparent.
1432 a way called a stighway, Hipperholme
1509 a styway goyng frome Crosseland to a house called the helme, Meltham. The OED has no references to ‘sty’ later than 1430, except in the alliterative phrase ‘by sty and street’. The EDD has ‘sty-road’ in Wakefield in 1865.