"outer upper covering of a house or other building," Middle English rof, from Old English hrof "roof," also "ceiling," hence figuratively "highest point, top, summit" also "heaven, the sky;" from Proto-Germanic *khrofam (source also of Old Frisian rhoof "roof," Middle Dutch roof, rouf "cover, roof," Dutch roef "deckhouse, cabin, coffin-lid," Middle High German rof "penthouse," Old Norse hrof "boat shed").
No apparent connections outside Germanic. "English alone has retained the word in a general sense, for which the other languages use forms corresponding to OE. þæc thatch" [OED]. Meaning "top of a carriage, etc." is by 1706. The meaning "upper part of the mouth, the hard palate" was in late Old English (hrof ðæs muðes). To raise the roof "create an uproar" is attested from 1860, originally in U.S. Southern dialect.
"provide a roof for, cover with a roof," early 15c., rofen, from roof (n.). Related: Roofed; roofing.