(( because the song is too pretty to ignore ))
Jack was certain that while everyone was feeling some sense of guilt or grief, his level of guilt differed. The two had bickered last they had been together and only barely had they 'made up,' something to the point of polite conversation. And yet Jack had to be here. Katara was the first person to greet him in this city of lost angels and torn people. The first to amaze him with her water bending abilities and to reassure him that while he was without anyone from his world (at the time), he was not alone. They had all been pulled without choice or reason and thus, they shared something.
He waited until no one else was near the railing before slow dragging himself forward. It wasn't that Jack didn't have a heart or was unaffected by Katara's death, it was he chose to not show it as much. He was hardly his lively, swaggering self, but he also kept the grief in check.
When he was sure no one could hear him, or at least he assumed, Jack softly sang for Katara, eyes locked on the water.
"Home is behind The World ahead And there are many paths to tread Through Shadow To the Edge of Night Until the Stars are all alight."
He gave a quick nod and moved away, heading back for home. Or at least his new home with William.