Correct usage calls for a strict division between sure (an adjective) and surely (an adverb). One says "That was a sure sign of his interest" and "That was surely a sign of his interest." In the first sentence, sure qualifies the noun sign; in the second, surely modifies the verb was. Sure can be employed informally as an adverb (sure enough), but this colloquial use is not recommended for careful writing. See also certain.
Dictionary of problem words and expressions. Harry Shaw. 1975.