Becker, George J. Shakespeare’s Histories. New York: Frederick Ungar, 1977.
Bloom, Harold. Shakespeare: The Invention of the Human. New York: Riverhead Books, 1998.
Boris, Edna Z. Shakespeare’s English Kings: The People and the Law. Rutherford, New Jersey: Fairleigh Dickinson University Press, 1978.
Council, Norman. When Honour’s at the Stake: Ideas of Honour in Shakespeare’s History Plays. New York: Barnes & Noble, 1973.
Desai, R. W. Falstaff: A Study of His Role in Shakespeare’s History Plays. India: Doaba House, 1976.
Shalvi, Alice. The Relationship of Renaissance Concepts of Honour to Shakespeare’s Problem Plays. Salzburg, Austria: University of Salzburg, 1972.
Watson, Robert N. Shakespeare and the Hazards of Ambition. Cambridge: Harvard University Press, 1984.
I think it should have been called Sir Jack, First Part, as Falstaff towers over everybody else in King Henry IV, Part 1. See my blog on the play:
Most Shakespeare plays have a jester, who is able to perceive certain things better than the "noble" person. There are other elements that make Falstaff more interesting, such as the juxtaposition of "fortune," class, or perhaps simply initiative.