Also this is an extension of the Jewish tradition of fasting on Tuesday/Thursday. AFAIK, the only reason the Church changed it was simply to distinguish themselves from the Jews during the height of the Judiazing heresey.
Wednesday fasting is to remember the betrayal of Jesus by Judas. Friday fasting to remember the Crucifixion. And of course there's fasting periods as well as weeks you don't fast at all. Monastics also fast an extra day of the week (Mondays), in addition to eating a more restrictive diet in general.
Friday fasting is a remembrance—and to a certain extent, identification—with the cruxifiction. Mild discomfort to commemorate a much stronger act of self-denial. It's documented as early as the 3rd century by Clement of Alexandria (Stromata VI.75) but as you point out it's a logical extension of a practice that was integrat to the Jewish tradition.
Also this is an extension of the Jewish tradition of fasting on Tuesday/Thursday. AFAIK, the only reason the Church changed it was simply to distinguish themselves from the Jews during the height of the Judiazing heresey.