I'm trying to find any record of the service of William M. Beezley (or Beasley) in the Black Hawk War. His family remembered that he had served in that war. He lost two sons in the Civil War, and his family recalled that William was a veteran of the B.H.W. when his widow applied for a dependant's pension in 1886.
I think that William probably served in an Illinois company, because census records show that his children were born in Illinois about 1831 and 1832, about the time of the war. However, he was married in Vermillion County, Indiana in 1830, and in 1840 he lived in Missouri.
Obviously there could be a lot of ways to spell "Beezley," although that and "Beasley" are the usual ones. I searched an on-line database of Illinois veterans, but was unable to find any mention of William, although I did see several other Beasleys and one Beezley, none of whom appeared to correspond with William.