Old English fæger "beautiful, lovely, pleasant," from Proto-Germanic *fagraz (cf. Old Saxon fagar, Old Norse fagr, Old High German fagar "beautiful," Gothic fagrs "fit"), perhaps from PIE *pek- "to make pretty" (cf. Lithuanian puošiu "I decorate").
The meaning in reference to weather (c.1200) preserves the original sense (opposed to foul). Sense of "light-complexioned" (1550s) reflects tastes in beauty; sense of "free from bias" (mid-14c.) evolved from another early meaning, "morally pure, unblemished" (late 12c.). The sporting senses (fair ball, fair catch etc.) began in 1856. Fair play is from 1590s; fair and square is from c.1600. Fair-haired in the figurative sense of "darling, favorite" is from 1909. First record of fair-weather friends is from 1736.