The weighty tomes that Hale brings with him to Salem are both literally and metaphorically heavy. Physically, they are enormous and over-sized. Figuratively, they are weighted with the authority of those who claim to be experts in the subject of witchcraft. At this stage in the play, Hale is still incredibly naive. He seems to think that consulting one of his learned volumes is all you need to do to identify a witch.
But as he will soon discover, the judicial authorities of Salem have their own ideas of what constitutes a witch, ideas that they didn't get from any book. Hale comes to realize that there are all kinds of factors involved in the witch-trials—personal, social, economic—that have nothing whatsoever to do with what's written down in any book. No matter how weighty, learned, or erudite Hale's books may be, they cannot capture the social and political complexity of the witch-hunting hysteria. Hale's book-learning has run up against the harsh realities of small town political life, and it's a sobering, disillusioning experience for him.