This article is from the alt.usage.english FAQ, by Mark Israel misrael@scripps.edu with numerous contributions by others.
"Tip", in the sense of "gratuity", does NOT stand for "to insure
[i.e., ensure] politeness/promptness" or "to improve performance".
It may derive from "tip" in the sense "to tap, to strike lightly"
or in the sense "extremity", both of which have cognates in other
Germanic languages. Or it may be a shortening of "stipend".
 
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