I'm referring specifically to phrases like, "kissing and shit" or "baseball and shit". Sometimes it is contracted: "n'shit".
"And stuff" has been used in this way since the late 17th century, according to Green's Dictionary of Slang.
The OED has this definition:
Worthless ideas, discourse, or writing; nonsense, rubbish. Often coupled with nonsense (chiefly stuff and nonsense, †nonsense and stuff)
with attestations from the 16th century, followed by this:
phr. —— and stuff, and such-like useless or uninteresting matters. colloq
with attestations starting at the end of the 17th century.
For "and shit", Green's has this:
[1960s+] (orig. US black) a general abstract term, usu. thrown into the end of a sentence, similar to you know phr.
(Two earlier uses are also relevant here to see the sense development: "any inferior, rubbishy, shoddy or pretentious thing" from the 1920s, and "any thing (material or otherwise), irrespective of its actual quality, ‘stuff’" from the 1930s.)
The OED's definition is:
orig. U.S. and shit: and so on; and similar stuff. Also used simply for emphasis
with attestations starting in 1965.
Thus, it seems certain that "and stuff" is the earlier expression, and "and shit" is simply a cruder synonym that has been introduced. Of course, with the history forgotten, "and stuff" may now be perceived (and used) as a euphemism for "and shit".
We learn our language from our others close to us which includes parents sibling, friends and associates. Perhaps since the strong survive and the weak go to the wall, it may include the desire to appear tough. Before universal education it is possible that the expression did not exist. This expression may also indicate the social milieu to which the user belongs or with which he/she may wish to be associated.