When and under what circumstances did the word "halakhah" (also spelled "halacha", "halachah" or, in Hebrew, הלכה) come to mean Jewish law?
I assumed it is based on the word הלך, going. Much as we would say inn English, 'I'm going with him' as a term of agreement. I checked Jastrow and he seems to take this route as well. First writing הלך as the שורש, than comparing it to מנהג and translating it accordingly. Practice, adopted opinion, rule. He does the same for הלכתא. He even quotes a Targum on Mishlei which uses הלכתיה to mean walking.
It is a common talmudic expression (see e.g. Brachos 6b).