An Etymological Dictionary of the German Language/Annotated/Rost
Rost (1.), masculine, ‘grate, gridiron,’ from Middle High German rôst, masculine, ‘grate, funeral pile, glow, fire,’ Old High German rôst, masculine, rôsta, feminine, ‘small gridiron, frying-pan,’ The current derivation from Rohr, in which case we should have to assume ‘iron grating’ as the primitively sense of Rost, does not satisfy the meaning (Old High German rôstpfanna, Middle High German rôstpfannue). Derivative rösten, ‘to roast, broil,’ Middle High German rœsten, Old High German rôsten, ‘to lay on the gridiron, roast’; hence the Romance cognates, Italian arrostir, ‘to roast,’ French rôtir, and from this again comes English to roast.
Rost (2.), masculine, ‘rust, mildew, blight,’ from Middle High German and Old High German rost, masculine, ‘rust, aerugo, rubigo’; corresponding to the equivalent Old Saxon rost, Dutch roest, Anglo-Saxon rûst, English rust (Scotch roost), For Gothic *rū̆sta-, ‘rust,’ nidwa, feminine, was used. Rost belongs to the Teutonic root rū̆d (pre-Teutonic rudh), ‘to be red,’ appearing in Modern High German rot. From the same root was formed the equivalent Old High German rosamo, which assumed early in Middle High German the meaning ‘freckle,’ as well as Old Icelandic ryð, neuter, Middle High German rot, masculine and neuter, Old Slovenian rŭzda (for rudja), feminine, Lithuanian rûdis (rudė́ti, ‘to rust’), Latin robigo, ‘rust’; also Lettic rûsa, ‘rust,’ rusta, ‘brown colour.’