It’s obvious that Weddell was well-read on the history of the region he explored (cf. his translation and abstracts of earlier Spanish reports, on p. 61-9), but this isn’t evidence of books aboard—he does speak of the credibility of some books inducing him to search certain islands, implying that copies were on the ship. And the obligatory prayer-books on British ships were certainly present.
David H. Stam's Anthologies of the Reading Experience