Although most and mostly are adverbs meaning "almost entirely," "for the most part," they are not always interchangeable. When the desired sense is "extremely" or "to the greatest degree," most should be used: "Those most influenced are young children." In the sense of "in the main" or "on the whole," mostly is preferable: "The marchers were mostly weary." (If you mean the marchers were utterly exhausted, say "most weary.") See also almost.
Dictionary of problem words and expressions. Harry Shaw. 1975.