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.