Like "Petition": I signed a 'petition,' and carried it onward to 'petition' for support of lower wages & more suffering etc.
A verb derived from a noun with the same pronunciation is "denominal". There is a difference in English between the stress patterns of verbs and nouns: nouns (and adjectives) can have two contiguous unstressed syllables, but "real" verbs cannot. Compare the noun "advocate", with stress only on the first syllable, with the verb "advocate", with stress on the first and third syllables. The noun has two contiguous unstressed syllables, "-vo" and "-cate", but the verb has only a single unstressed syllable, the "-vo".
However, verbs that have the same pronunciations as nouns, denominal verbs, are atypical in this regard. If the noun has two contiguous unstressed syllables, then so must the verb. "calendar" - to note an event on the calendar. "colander" - to put food through a colander.
The sense of derivation here, for denominal verbs, has nothing to do with the history of words.