Walton is obviously skeptical about the story he has heard, but he is empathetic to Victor and his traumatized life. The appearance of the creature at Victor's bedside proves the verity of the tale, and so it is understood that Walton believes what Victor has told him. There is also evidence that Robert Walton has learned from the story since he does decide to turn back when his crew threatens mutiny. Frankenstein, blinded by ambition, would not have given in to the wishes of his loved ones or co-workers when he was Walton's age.
In his letter to his sister Margaret, dated August 26th, 17--, Walton tells her that he has listened to the "strangest tale that ever imagination formed." Continuing, Walton relates how absorbed he has been by this tale, and how impressed he has been by the "elevated and gentle manners" of Victor Frankenstein, who has touched him deeply.
Because Walton has heard the history of Victor Frankenstein, he amends his statement in his fourth letter that his venture is important enough that a few lives are worth the cost--"a small price to pay for the acquirement of knowledge." Instead, he now tells his sister that
it is terrible to reflect that the lives of all these men are endangered through me. If we are lost, my mad schemes are the cause.
Thus, it is because of his warm relationship with Victor Frankenstein that Walton becomes more prudent regarding his venture, listens to his crew, and turns back, heading home.
Of course, Walton does not hear all of the new friend's story until the end of the book. After the 4th letter home to his sister, the rest of the book is the new friend's (Victor's) story.
However, in the fourth letter home, Walton talks a great deal about how his new friend makes hiim feel. Walton has been a very lonely man and is very happy to have a new friend. He says that Victor's problems fill him with compassion and sympathy because of how sad Victor is.
So what Walton knows of the story so far makes him feel a lot of sympathy for Victor. He wants very much to hear the rest of his story but he does not want to push Victor too much.