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 Places (2000):

Sweeny, TX -- U.S. city in Texas
   Population (2000):    3624
   Housing Units (2000): 1444
   Land area (2000):     1.861690 sq. miles (4.821754 sq. km)
   Water area (2000):    0.000000 sq. miles (0.000000 sq. km)
   Total area (2000):    1.861690 sq. miles (4.821754 sq. km)
   FIPS code:            71492
   Located within:       Texas (TX), FIPS 48
   Location:             29.042923 N, 95.699956 W
   ZIP Codes (1990):     77480
   Note: some ZIP codes may be omitted esp. for suburbs.
   Headwords:
    Sweeny, TX
    Sweeny