The Good Son/WMG

Henry didn't kill Richard
Or, at least, he didn't mean to kill Richard. Richard's accidental death was what caused Henry to snap and eventually turn into a sociopath. Later, he chose to take credit for his brother's death.
 * Any WMG on Henry's motivations would be putting more thought into the subject than the filmmakers did.
 * Sociopathy doesn't work that way. People don't turn into sociopaths, they just are born without a conscience.
 * Actually, I'm pretty sure mental illness is acquired just as much if not moreso than it is innate.
 * "Pretty sure" doesn't hold a candle to scientific evidence. While there are some theories which say that sociopathy could be developed from growing up in an environment that doesn't establish a sense of right and wrong for the child to follow, Henry doesn't seem overtly spoiled and I think it's obvious to anyone watching the film that he doesn't live in a ghetto. The only logical conclusion is that he was born with an inability to feel empathy. The whole "he lost the ability to care about human suffering because a death traumatized him" thing is...actually a lot stupider than the movie. Not every crazy killer needs a Freudian Excuse. Some kids are just born bad.
 * Except sociopath =/= evil serial killer type in every instance, or even a lot of the time. Most sociopaths never do anything more sinister than be insensitive and carry out mean actions when not afraid of reprisal, and even a lot of the ones who are considerably worse aren't exactly killing multiple people at ten years of age - at that age even most future serial killers are still torturing animals. I'd modify this theory by saying Henry was always a sociopath, but the little brother's death gave him a fascination with death, which is actually pretty normal for a kid whose lost a family member, but since he already had no empathy it made his sociopathy take on a much more dangerous form, so that if the baby hadn't died the movie would be about Mark, a kid in mourning who had the misfortune of having to spend his mourning period with his jerk of a cousin who wouldn't quit making insensitive comments about his dead mother and picking on his younger family members. It's still a longshot but somewhat better than assuming this is just The Theme Park Version of sociopathy.

The last shot of him after he fell, showed no sign of blood or any splatter when he hit the rock and the water simply swept him away.
 * I dunno, that rock looked pretty fucking red to me.
 * It was red alright. There was some red in the water as well. So I think it's safe to assume the fall did kill him.
 * True but the red did look more like rust than blood.

Henry is The Stepfather.
The fall didn't kill him but it gave him amnesia and a murderous urge when it came to family. Not to mention the first Identity of The Stepfather before he changed it was Henry.
 * Or he could very well be Henry Lee Lucas.