"tip"

     [This is a fast-access FAQ excerpt.]
"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".