Pete literally drags Norton across the brutal landscape, handcuffed and barefoot. Norton is beaten, starved, sunburned, drowned, snakebit, starved, burned, and beaten some more. All we know for sure is that Pete wants to keep Norton alive long enough to make him bury Melquiades. This act will fulfill Pete's friendship to Melquiades, but will Pete decide that Norton has repaid his debt to Melquiades? It doesn't matter that the shooting wasn't murder per se. Before Pete abducts him, we see that Norton is torn apart with self-loathing for this shooting. The abduction and journey are a simple metaphor for what Norton's doing to himself on the inside. Only when Pete forces him to seek forgiveness (at gunpoint) does Norton unload his grief.
NOTE: Emily proposed this movie. I offered to go to the Capitol Theater and see Match Point while she saw Three Burials. When we got to the theater, the Match Point screening had been canceled due to a projector problem, so I joined Emily for The Three Burials of Melquiades Estrada.