what sources of evidence does Max Weber use to show a relationship
between the Protestant ethic and the spirit of capitalism? A focus on
Franklin and methods

Here are some useful articles that should provide you with the
information you are seeking:

"Weber hypothesized that capitalism was a product of the western mind
for a number of reasons, not the least of which was the Protestant
Ethic. The Protestant Ethic spawned and encouraged what Weber called
the "spirit of capitalism." By Weber's definition, this is more than
simply capitalist activity. It is, in fact, the essence which
underlies the economic system. During the long 16th century, this
spirit became embodied in European society and provided the impetus
for capitalism to emerge as the dominant economic system in the world.

For Weber, capitalism was more than simply an accumulation of wealth.
It had in roots in rationality. In fact, Weber insisted that
capitalism was the triumph of rationality over tradition. Explicit in
his view of capitalism were a disciplined labor force and the
regularized investment of capital. Weber asserted that this
combination took place only in Europe and most strongly in Protestant
nations, such as England, Holland, and Germany, where there were
influential groups of ascetic Protestant sects.

Weber was influenced by the writings of Benjamin Franklin, in which he
saw early indications of the spirit of capitalism before there was a
capitalistic order in the American colonies. Weber quoted Franklin
early in his work and based many of his ideas on Franklin's
writings...."

From:  "The Protestant Ethic and the Spirit of Capitalism: Criticisms
of Weber's Thesis" by Sandra Pierotti
http://www.ecs.gatech.edu/support/sandra/paper.html

Additional materials:

"The Protestant Ethic and the Spirit of Capitalism" Wikipedia (June
13, 2005) http://en.wikipedia.org/wiki/The_Protestant_Ethic_and_the_Spirit_of_Capitalism
provides a concise summary of Mr. Weber's work in this area.

Goldenessays.com http://www.goldenessays.com/free_essays/4/sociology/protestant-ethics-of-webber.shtml
provides another summary of Mr. Weber's ideas and their development.

Max Weber, The Protestant Ethic and the Spirit of Capitalism. New
York: Scribner's Press, 1958, pp. 47 - 78.
http://www2.pfeiffer.edu/~lridener/DSS/Weber/PECAP.HTML.  This site
reproduces several pages of Mr. Weber's book.  This portion deals
extensively with Benjamin Franklin.

Search Terms: Max Weber Protestant Franklin

Sincerely,

Wonko

"what sources of evidence does Max Weber use..."
It would seem that these would be evident in his book, if you read it.