First, please keep in mind that this is an opinion question. This means that there is no “right” answer, but the reader can make his or her own decision as to who the healthiest person is at the end of the story. The reader can then support his or her decision with examples from “The Things They Carried.” The other issue with your question is that a person can be in perfect physical shape while being mentally, emotionally, or spiritually unstable. If you are referring someone being physically healthy, then the answer to your question is any character that is not dead, dismembered, or wounded. I am going to assume that you are talking about mental and emotional health. In my opinion, the healthiest person (mentally) is the narrator of the story: Tim O’Brien.
Although all of the characters who survive in “The Things They Carried” have Post Traumatic Stress Disorder, it is only Tim O’Brien who heals greatly through his narration of the story. He does this by remembering the lives of the dead. In these stories, he makes the dead feel “not so dead.”
I can see Kiowa, too, and Ted Lavender and Curt Lemon, and sometimes I can even see Timmy skating with Linda under the yellow floodlights.
Later, Tim O’Brien shifts the focus to himself completely. He imagines himself “young and happy.” He is exploring his “own history” within his writing. He is healing through the words. But perhaps the thing that heals Tim O’Brien the most (and makes him the most mentally healthy character), is that he helps the dead be remembered. This relieves his guilt.
When I take a high leap into the dark and come down thirty years later, I realize it is as Tim trying to save Timmy’s life with a story.
By helping the dead be remembered, O’Brien talks here about saving his own life. In this way, he becomes the most mentally healthy character.