The reader is never meant to be sympathetic to Tom OR his wife. In the second paragraph, Washington Irving tells us that Tom's wife was,
"....fierce of temper, loud of tongue, and strong of arm.......his face sometimes showed signs that their conflicts were not confined to words."
They are both described as meager and cheap. She took the household valuables to negotiate with the dark stranger. When she didn't return, the story tells us
"....Tom Walker grew so anxious about the fate of his wife AND HIS PROPERTY that he set out at length to seek them BOTH...." (paragraph 32)
When he finds the body of his wife hanging from a tree with a vulture nearby, he,
"....leaped for joy, for he recognized his wife's apron and supposed it to contain the household valuables" (paragraph 32)
"Let us get hold of the property,' said he, consolingly to himself, and we will endeavour to do without the woman." (paragraph 33)
The reader should not be surprised by this reaction. Tom and his wife have never gotten along, have had loud conflicts, and obviously have dealt separately concerning their property. The storyteller tells us that all that was found in the apron was a heart and a liver. Evidently she had tried to treat and argue with the "black man" the same as she did with her husband. Wrong choice on her part.
Tom was not that upset, however. In fact, he felt,
"....something like gratitude towards the black woodsman, who he considered had done him a kindness." (paragraph 36)
Personally, I was not surprised at Tom's reaction. His wife was not a loving person. She was not even the least bit loveable. Throughout the whole story, he was concerned about his property and the only thing he really mourns is the loss of his property, but at least he doesn't have to share it with her anymore. You will notice that he never remarries because that would mean sharing his wealth. He doesn't have to share his wealth with her,he doesn't have to deal with her abuse, and he doesn't have to worry about her giving away his property. It just fits his personality.