Differences from the book
It didn't make any sense to me that people would think Wade was the father of Libby's baby. I also didn't think Theron's "I never want to get married" was enough to discourage Libby from telling him she was pregnant. In a way, it was selfish of her, because she's letting another man raise Theron's child.
There were a lot of changes from the book.
There is no Rafe. Theron was never a mama's boy although he was innocent and naive. He was close to both parents, separately, in different ways. Wade taught him to track and hunt from an early age and Theron idolized him.
Theron became distant with Libby because of his mother. Theron was upset that Libby's father didn't like him. He told Hannah. Hannah couldn't bear to have Theron think it was because of anything in Theron's character, so she told him it was because of his father's womanizing. Theron already felt guilty about having sex with Libby, and he feared that he was just like his dad, that it was "in his blood". This is confirmed for Theron one night when he got drunk and visited a prostitute.
Hannah told Wade about Libby's father (Albert) refusing to let Theron see Libby. Wade confronted him -- in front of townspeople -- and Wade backed down. (People remember this later, after Libby has her baby.)
Libby's father sends her away to college. When she finds out she's pregnant, she takes a bus home, shows up in the middle of the night and tells her parents, but she doesn't tell them who the father is. That same night, Libby's father goes to see Wade. He does this because he thinks Libby has gotten pregnant by a college boy, and he wants to make things up with Wade, thinking that maybe Libby and Theron can get together, Theron being a better candidate for baby daddy than some uppity college boy.
Wade, not knowing that Theron is really the baby's father and thinking Albert wants to trap Theron, tells him the family doesn't want "damaged goods". Albert leaves the house, crying, and a friend of Albert's sees him.
The next day, Libby goes to the Hunnicutt house to see Theron. It seems they're on the verge of making up, but before Libby can tell Theron she's pregnant, Theron tells Libby he's done bad things and he's not worthy of her. (Theron's guilty about the prostitute.) At this point, a young woman comes out of the house -- a woman who's been staying with the Hunnicutts. Libby sees the woman and thinks Theron has moved on, that he doesn't love her anymore. They part.
The woman who's staying at the house is Opal, the mistreated wife of one of Wade's tenant farmers. She has a baby, and Hannah thinks the baby is Wade's. It's not. Theron thinks the baby is Wade's, and looks at him as a brother.
Within a few days, Libby seduces an old boyfriend. They're at the courthouse getting married, and Theron sees them. At the same time, Opal is at the courthouse getting a divorce from her husband. Theron wants to atone for his father's "sin", so he marries Opal, but never sleeps with her.
Fast forward to the birth of Libby's baby, a nine-pounder after a seven month marriage. Townspeople note that the baby has the Hunnicutt look. They start to suspect Wade (naturally) and Albert's friend remembers seeing Albert leaving the Hunnicutt house seven months earlier, in tears. At the baby's christening, Albert hears the gossip and thinks about Wade's "damaged goods" comment, and comes to believe Wade is the father.
He goes to Wade's house and kills him. Theron tracks Albert down and kills him. Theron disappears. End of story.
The graveyard scene at the end, of course, doesn't happen. There was no illegitimate child (Rafe) for Hannah or Wade to accept.
What does happen in the graveyard is at the start of the book. It's 15 years since Wade's death. Hannah has died. Her body is brought to the graveyard where there are three tombstones, one each for Wade, Hannah, and Theron. The death dates for Wade and Theron are the same, even though there's no body in Theron's grave, and the townspeople know it.