c. 1300, "main road, highway," from Old English heafodweg; see head (adj.) + way (n.). Sense of "motion forward" first attested 1748, short for ahead-way; ultimately nautical (compare leeway).
the ship made little headway against the gale
headsman
headstone
headstrong
heads-up
headwaters
headway
heady
heal
heal-all
healer
healing