I know this is an old post but I feel I must provide another perspective, because it seems to me that many people miss the fact that Vader actually strikes an empty cloak. The Jedi, Obi-Wan has vanished before the strike.
I'll describe the scene for you: As our heros approach the falcon (Luke, Leia, Han, Chewie and the droids) the stromtroopers are distracted by the duel and abandon their post. The heroes rush out to the falcon when Luke spots Ben and Vader. At this point Ben has already uttered the quote from the OP and now as he spots Luke, he pauses, smiles, raises his sabre to a vertical position, holds it in front of his face and closes his eyes in concentration. Vader swipes, but suddenly there is no more Ben. He has completely vanished. This is in stark contrast to all other sabre duels, where the bodily remains are always left behind.
a youtube clip (the video is perhaps a few seconds shorter than a would've liked though, becuase afterwards Vader even steps on the cloak and prods it with his toes, because he is confused that Obi-Wan has vanished)
And from the script itself (albeit an early draft, but this scene is consistent with what we still see in the film today). Emphasis, mine:
The old Jedi Knight looks over his shoulder at Luke, lifts his sword
from Vader's then watches his opponent with a serene look on his face.
Vader brings his sword down, cutting old Ben in half. Ben's cloak
falls to the floor in two parts, but Ben is not in it. Vader is
puzzled at Ben's disappearance and pokes at the empty cloak. As the
guards are distracted, the adventurers and the robots reach the
starship. Luke sees Ben cut in two and starts for him. Aghast, he
So, to answer the question: why does Obi-Wan say he will become more powerful? Because that is part of his vision and his plan. In order to provide ongoing guidance to the rebellion's last hope, Luke, this is what must happen. Does Vader actually kill him? That is debatable, but in light of previous duels between Obi-Wan and Anakin, perhaps Ben has decided that neither one of them can defeat the other because they are too well matched against each other. He simply gives in to the force, transcends to his next spiritual being and lives on.