Sieg Heil (interj.)

masc. proper name, German Siegfried; the first element is from Old High German sigu "victory," from Proto-Germanic *seges- "victory" (source also of Old Frisian si, Old Saxon sigi, Middle Dutch seghe, Dutch zege, German Sieg, Old Norse sigr, Danish seier, Gothic sigis, Old English sige "victory, success, triumph"), from PIE root *segh- "to hold" (source also of Sanskrit saha- "victory," sahate "overcomes, masters").

The second element is from Old High German frithu "peace" (from suffixed form of PIE root *pri- "to love"). Siegfried Line, World War I German fortifications in France (and German western defenses after it), is from German Siegfriedlinie, named for the hero in Wagner's "Ring" cycle.

Old English hælþ "wholeness, a being whole, sound or well," from Proto-Germanic *hailitho, from PIE *kailo- "whole, uninjured, of good omen" (source also of Old English hal "hale, whole;" Old Norse heill "healthy;" Old English halig, Old Norse helge "holy, sacred;" Old English hælan "to heal"). With Proto-Germanic abstract noun suffix *-itho (see -th (2)).

Of physical health in Middle English, but also "prosperity, happiness, welfare; preservation, safety." An abstract noun to whole, not to heal. Meaning "a salutation" (in a toast, etc.) wishing one welfare or prosperity is from 1590s. Health food is from 1848.