The Collaborative International Dictionary of English v.0.48:

Sweeny \Swee"ny\, n. (Far.)
   An atrophy of the muscles of the shoulder in horses; also,
   atrophy of any muscle in horses. [Written also swinney.]
   [1913 Webster]

U.S. Gazetteer (1990):

Sweeny, TX (town, FIPS 71492)
  Location: 29.04535 N, 95.69933 W
  Population (1990): 3297 (1286 housing units)
  Area: 4.7 sq km (land), 0.0 sq km (water)
  Zip code(s): 77480