In The Crucible, what is the significance of the remark "They must be heavy; they are weighted with authority" ?

This quote employs the use of a pun. A pun is at work any time a
word can have two different meanings. Often, one meaning is the denotative meaning which is the
literal or dictionary definition. In this case heavy and
weighted both refer to the literal fact that the books are large and likely
weigh several pounds. The other meaning is the connotative meaning, the understood meaning
because of slang or a figure of speech that both parties would likely use. In this case, these
two words reference the depth of spirituality that the books contain. Figuratively, Hale is
claiming a great amount of God's authority rests within these particular
books.

Another noteworthy aspect of this quote is the circumstances
under which it is said. Rev. Hale says this to John Proctor after Proctor notices how large and
numerous the books that Hale brings actually are. John likely meant his comments as a jest, Hale
takes in jest as literal and responds with confidence in the job he is about to do in releasing
the afflicted girl from the evil spirit which possesses her. This builds suspense and conflict as
Proctor is almost questioning the authority of Hale. As you see the close of the play, you'll see
that Proctor had good reason to doubt.