All 3 Uses of

petty
in
The Scarlet Letter

The founders of the greater part of the families which now compose the aristocracy of Salem might here be traced, from the petty and obscure beginnings of their traffic, at periods generally much posterior to the Revolution, upward to what their children look upon as long-established rank, Prior to the Revolution there is a dearth of records; the earlier documents and archives of the Custom-House having, probably, been carried off to Halifax, when all the king's officials accompanied…
p. 28.7

petty = unimportant

These supplied material for petty activity to a mind that would otherwise have been eaten up with rust.
p. 30.4

petty = insignificant (unimportant)

...to seek, resolutely, the true and indestructible value that lay hidden in the petty and wearisome incidents, and ordinary characters with which I was now conversant.
p. 36.7 *

petty = unimportant

Definitions:

(1) (petty as in: a petty crime)
of less importance -- at times implying insignificance
(2) (petty as in: don't be petty)
unpleasantly focusing on an unimportant flaw; or attempting to make someone suffer for an unimportant wrong
(3) (petty as in: petty officer)
a non-commissioned officer

Petty officer typically refers to a Navy or Coast Guard officer who is subordinate to commissioned officers and chief petty officers.