The Collaborative International Dictionary of English v.0.48:

Reedy \Reed"y\ (r[=e]d"[y^]), a.
   1. Abounding with reeds; covered with reeds. "A reedy pool."
      --Thomson .
      [1913 Webster]

   2. Having the quality of a reed in tone, that is, harsh and
      thin, as some voices.
      [1913 Webster]

U.S. Gazetteer (1990):

Reedy, WV (town, FIPS 67660)
  Location: 38.89881 N, 81.42719 W
  Population (1990): 271 (120 housing units)
  Area: 0.6 sq km (land), 0.0 sq km (water)
  Zip code(s): 25270