Some of these observations might exactly answer the question. In the eighteenth and nineteenth centuries, some of the basic populations in many parts of the US were English, Scots-Irish, and German. (Indeed, German was so widely spoken in the eighteenth century that there was an attempt to translate government documents into German in 1795, prompting the country's first "official language" debate. It was still so widely spoken in the twentieth century that a major TV personality--Lawrence Welk--had a strong German accent, despite having been raised entirely in the American Midwest.) All of these groups used Willie or Willy sometimes as the diminutive of a common name. So it was indeed a good possibility for a "regular American" name for over 200 years.