Why the poor viola should be the butt of jokes is not clear, though it's interesting that composer Richard Strauss, who assigned the part of Don Quixote to the cello in his tone poem of that name, gave the role of the comical Sancho Panza to the viola. Other than that, it's not a funny instrument. The violas also have moments of glory in symphony orchestras. For instance, one of Rachmaninoff's most famous and beautiful melodies, in the third movement of his Second Piano Concerto, is introduced by the violas. And the violas, though they are very subdued, open Mozart's great Symphony No.40 in G minor.
People cry when they chop an onion to pieces.
Barbara Hustis and Ann Marie Hudson, the two associate principal violists of the Dallas Symphony Orchestra, think that viola jokes became popular because violists have a sense of humor. The fact that one of the best viola-joke sites on the Internet is run by a viola player tends to back them up. The viola was developed about the same time as the violin, about 1500. They have a similar shape and are held almost the same way, but the viola is pitched a fifth lower. Compared to the human voice, the violin is the soprano and the viola is the alto.