"Irish Names and Surnames," collected and edited by Rev. Patrick Woulfe, states (pp. 571-572) that Healey, Hilley, Hilly, and Hillee is a variation of a Gaelic name written - more or less - as O'Fiheallaig. Apparently in Gaelic, the letter F is aspirated, i.e., pronounced with an H sound in front - "HF." Our ancestors anglicized this name by dropping the F and keeping the H - others dropped the H and kept the F, and became Fields and Feely.
Those keeping the H were found in County Kerry, near Tralee, in the 1500s. The Feelys were in southwest County Cork. According to Rev. Woulfe, the original name meant "chess-player."