In the end, it wasn't that Peter Pettigrew felt like the other boys looked down on him, it wasn't that he was tired of being second best, it wasn't even that he disliked them or sympathized with the Dark Lord. No one had been whispering in his ear- he made the choice himself. He hated himself for it, but it was for the Greater Good.
The reason for his betrayal was a prophesy Sibyll Trelawney made. But it wasn't the Chosen One prophecy. It was different and it went like this:
Chosen as a lion,
For his love of all that's good
Bonded tight in friendship
Doing all a good friend should
Betraying those who love him
And those he loves back
To save the world
From a Dark Lord's attack
Sacrificing the innocent
To kill their greatest bane
Never to reveal his innocence
Always to take the blame
To raise the one he conquered
As to bring him to his knees
The bravest of the brave
Doing all he should
Because its all
For the Greater Good
Peter Pettigrew was no fool. He pieced together what it meant with a few clues. He had to betray his friends so the Dark Lord would fall. He almost didn't do it but in the end he knew he had to. He didn't want Sirius to end up in Azkaban, but when he cornered him he had no choice. The prophecy told him he had to appear guilty to those that mattered. And that's what he did. It killed him to kill that boy Cedric but he did. It killed him to hurt Harry, but he did. In the end, when Voldemort's gift turned on him, he was glad. He was glad to die, to sleep into oblivion and know no more.
Perhaps Lily and James would forgive him. He was less confident Sirius would, but Peter didn't think he deserved any forgiveness at all. He betrayed them in the end, even if he did it for the right reason. It was after all, the height of dishonor to betray one's friends.