The "fat man" is meant to offer the ultimate justification in sending boys and soldiers off to war. His rationale in how parents must deal with their children going off to fight lies in the idea that the "love of country" must override all else. In this light, parents and loved ones must take solace in the fact that "the ultimate sacrifice" is a revered one, a rationale that precludes all suffering, all inquiries, and all questioning. His role is to support that of the state, to offer the government's line of argumentation in attempting to answer how parents can willingly stand by and send their children off to die in a war that lies outside of the control of the body politic. While he eloquently offers a rationale, it is undercut by the woman's question that sends him into an uncontrollable terrain of sobbing and sadness. In the end, his purpose is to prove that while many can seek to justify war, few, if any, can really substantiate the breaking of a parent's heart.
The fat man is supposed to represent people who really approve of the war. Or at least that is what it seems like at first.
He seems this way because what he says seems to be a very extreme view in favor of the war. He is, basically, saying that the country is more important than anyone's family or any kind of personal considerations.
But then he shows that he does not really believe what he has been saying. To me, then, his real role is to deny the validity of the point of view he gives at first. I think he is meant to argue that those ideas are totally invalid.
The "fat, red-faced man with bloodshot eyes" at first seems to be a spokesman for the war and the military. Even when he discloses that his "son, before dying" (paragraph 21) expressed satisfaction that his death was really a happy one, this man seems to consider warfare in the abstract. His true feelings, however, emerge when the question of the woman in the corner actually forces him to realize that his son is truly dead, and that his son was a beloved son, not a representative of the government. It is the immediacy of his realization, and his sobs, that bring the story to its powerful conclusion.