Halfway means at the middle point between two places or two times. Neither here nor there.
It works as an adverb and an adjective, so stopping halfway and the halfway point are both standard. There is a strong figurative use about compromise, since meeting somebody halfway means each side giving a little, and it is one of the most useful phrases in any negotiation. A halfway house is both a building for people leaving institutions and any partial solution.
1adverbhalfwayAt or to the middle point of a distance or period.
“We stopped halfway and had lunch.”
Old English
healfweġ — half-way
Middle English
halfwey
English, today
halfway
From Middle English halfwey, from Old English healfweġ (“half-way”), equivalent to half- + way. Compare partway. Cognate with stq hoolfwais (“halfway”), Dutch halfweg (“halfway”), German halbwegs (“halfway”), Danish halvvejs (“halfway”), Swedish halvvägs (“halfway”).
Etymology from Wiktionary, CC BY-SA