Why does Paul laugh uncontrollably over Billy Boy dying in "Where Have You Gone, Charming Billy?"

Tim O'Brien's short story "Where Have You Gone, Charming Billy?" is the tale of Private First Class Paul Berlin's first night of the Vietnam War as he and his platoon march through the countryside toward the coast. The two recurring themes in the story are Paul's fear and the death of fellow soldier, Billy Boy Watkins, who died of a heart attack that afternoon.
The platoon marches silently, trying to avoid the notice of enemy forces. Paul is therefore left alone with his thoughts in the dark, humid night—thoughts he is strenuously trying to avoid:

He was pretending he was not in the war, pretending he had not watched Billy Boy Watkins die of a heart attack that afternoon. . . . In the dark, with his eyes pinched shut, he pretended.

The men move single-file through the night without speaking, passing rice paddies, villages, and a graveyard. Paul follows obediently, though feelings of isolation persist.

The soldiers were quiet and hidden and faraway-seeming in a peaceful night, strangers on a long street, and he felt quite separate from them.

The silence, the darkness, and the foreign nature of Paul's surroundings, coupled with his sense of isolation, give the story a dreamlike feel, and the language is dense with references to sleep, dreams, and nightmares. The soldiers move "like sheep in a dream," and when roused from his thoughts, Paul shivers "as if emerging from a deep nightmare." It is only while "sleeping in his walking" that Paul's fear subsides, because his daydreams allow him to escape back to his family home or to a temporary oblivion. When he tries to engage with his surroundings, he cannot get any purchase on them: the stars overhead are strange and nameless, like the men in his platoon,

The string of shadow soldiers whose names he did not yet know moved with the silence and slow grace of smoke.

Everything is unreal to Paul, so it is natural to disengage and let his mind wander. His fellow soldier, however, emphasizes that Paul needs to stay alert despite the hypnotic nature of their milieu by saying,

You got a lot to learn, buddy. I’d shoot you if I thought you was sleepin’.

But Paul continues to drift into reveries as they march, even as he actively tries not to think. He counts his steps, he sings songs in his head, he imagines describing this place to his mother, and he imagines describing his actions to his father. He is attempting to distance himself from the reality he is moving through—to think of it in the past tense or not at all. He imagines things from a future perspective: "when he reached the sea," "after the war," "he would forget."
What Paul is trying to forget and distract himself from is the spectacle of Billy Boy Watkins's death. It intrudes on his thoughts throughout the story, although for most of it, the reader only knows that Billy Boy died of a heart attack—Paul's thoughts will not go further than that. It is when Paul is forced to engage with reality, in talking to Buffalo, that the memory of Billy Boy's death breaks through.
Billy Boy stepped on a land mine and blew off his foot. The pain and the fear he suffered caused his heart to fail. His body bag then fell out of the Medevac chopper into a rice paddy, and the soldiers had to spend the afternoon retrieving Billy Boy's corpse.
The scenario, from start to finish, is absurd, foolish, and sadly ugly. There is no dignity in Billy Boy Watkins's death, which should not have happened, anymore than his body should have fallen from a great height into a muddy, leech-infested paddy like a bundle of garbage. Death is sudden, unexpected, and weird. It is crude and stupid. No amount of retelling or distance will make the story of Billy Boy's death any less ridiculous, and it is the sheer absurdity of the situation which seems to terrify Paul the most. He has spent the entire day gripped by fear. At first, he felt completely paralyzed by it, but now he feels it to be "diffuse and unformed"—like mist. It surrounds him but does not prevent forward movement. His fear has become just another surreal element of the landscape to accept and ignore.
When Paul talks to Buffalo, a more experienced soldier, Buffalo wryly acknowledges the bizarre nature of Billy Boy's death:

Can’t get over it—old Billy Boy croaking from a lousy heart attack. . . . A heart attack—can you believe it?

He says Billy Boy was "tough as nails" and shakes his head at the thought of such a man succumbing to a heart attack—a heart attack which Doc Peret said was caused by fear:

He was scared he was gonna die—so scared he had himself a heart attack—and that’s what really killed him. I seen it before.

Confronted with the memory he has been trying to repress all day, Paul's fear ceases to be diffuse and takes on a distinct form: hysteria. Billy Boy was, like Buffalo, an experienced soldier, yet he "scared [himself] to death." No amount of experience could save him from his own terror, and nothing can make death more dignified. To really hammer the lesson home, Billy Boy's body "executed a long and dangerous dive [from the Medevac chopper], as if trying to escape Graves Registration," showing that the formal symbols of death (the registration, the flag-covered coffin, the telegram to family members) are nothing compared to the farcical reality of it. Paul's fear transforms into a kind of appalled hilarity, and he bursts out laughing thinking about it.

Giggling and remembering, he covered his mouth. His eyes stung, remembering how it was when Billy Boy died of fright.

His laughter now is compared to Billy Boy's crying that afternoon, showing that both are just symptoms of profound, unshakeable fear. No amount of reassurance or even sedation from Doc Peret could calm Billy Boy, and no amount of frantic warnings and shaking from Buffalo can stop Paul's hysterical giggling:

“Shut up!” the soldier hissed, but Paul Berlin could not stop giggling, remembering: scared to death.

It is only when Buffalo smothers him—literally deprives Paul of air—that Paul finally regains control of himself, distracted from his fear by the need to breathe. As the platoon marches on, Paul takes his temporary hysteria and uses it to distance himself from Billy Boy's death through humor, imagining it now as a "funny war story that he would tell to his father, how Billy Boy Watkins was scared to death. A good joke." As Buffalo tells him,

You got to stay calm, buddy. Half the battle, just staying calm.

Although Paul has discovered a coping mechanism, his fear does not go away and possibly never will.