An influential man, a big shot (see under big cheese), as in You'll have to get permission from big daddy. [Slang; mid-1900s]
A male sweetheart or friend, often a man considerably older than his female companion; a sugar daddy. [Slang; mid-1900s]
Grandfather. This usage originated in the South among African-Americans.
The largest or most important person or thing of its kind. For example, The United States has long been the big daddy of the Western Hemisphere, or The blue whale was the big daddy of the ocean. [Slang; 1960s]