The Collaborative International Dictionary of English v.0.48:

Fairly \Fair"ly\, adv.
   1. In a fair manner; clearly; openly; plainly; fully;
      distinctly; frankly.
      [1913 Webster]

            Even the nature of Mr. Dimmesdale's disease had
            never fairly been revealed to him.    --Hawthorne.
      [1913 Webster]

   2. Favorably; auspiciously; commodiously; as, a town fairly
      situated for foreign trade.
      [1913 Webster]

   3. Honestly; properly.
      [1913 Webster]

            Such means of comfort or even luxury, as lay fairly
            within their grasp.                   --Hawthorne.
      [1913 Webster]

   4. Softly; quietly; gently. [Obs.] --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

fairly
    adv 1: to a moderately sufficient extent or degree; "pretty
           big"; "pretty bad"; "jolly decent of him"; "the shoes are
           priced reasonably"; "he is fairly clever with computers"
           [syn: reasonably, moderately, pretty, jolly,
           somewhat, fairly, middling, passably] [ant:
           immoderately, unreasonably]
    2: without favoring one party, in a fair evenhanded manner;
       "deal fairly with one another" [syn: fairly, fair,
       evenhandedly]
    3: in conformity with the rules or laws and without fraud or
       cheating; "they played fairly" [syn: fairly, fair,
       clean] [ant: below the belt, unfairly]

Moby Thesaurus II by Grady Ward, 1.0:

109 Moby Thesaurus words for "fairly":
   a bit, a little, absolutely, acceptably, actually, adequately,
   after a fashion, appreciably, at any rate, at best, at least,
   at most, at the least, at the most, at the outside, at worst,
   comparatively, completely, decently, decipherably, deservedly,
   detectably, disinterestedly, dispassionately, duly, equally,
   equitably, evenly, extremely, fair, fair to middling, fairishly,
   fairly well, honestly, impartially, impersonally, in a manner,
   in a measure, in a way, in part, in some measure, incompletely,
   indifferently, justifiably, justifiedly, justly, kind of,
   leastwise, legibly, mediocrely, meetly, merely, middling well,
   middlingly, mildly, moderately, modestly, more or less,
   not comprehensively, not exhaustively, objectively, only, part,
   partially, partly, passably, positively, presentably, pretty,
   pretty well, pro tanto, properly, purely, quite, rather, readably,
   really, relatively, respectably, rightfully, rightly,
   satisfactorily, scarcely, simply, slightly, so far, so-so, some,
   something, somewhat, sort of, sufficiently, thus far, to a degree,
   to some degree, to some extent, tolerably, totally,
   unexceptionably, upon even terms, utterly, veritably, very,
   virtually, visibly, warrantably, warrantedly, well enough,
   without distinction