To fully understand the boy's reaction to Santiago's catch, it is important to consider it in the context of the relationship between them that the author establishes in the beginning of the novella. It is clear from the start that the boy deeply loves Santiago. He used to fish with the old man and learned how to fish from him, but when they didn't catch anything for a long time, the boy's parents proclaimed Santiago unlucky and insisted that he should work in another boat.
As the story opens, the boy tells Santiago that he has money now and he could accompany him again. However, Santiago counsels the boy to stay with his current boat because it is lucky. Santiago and the boy share a beer on the Terrace, and the boy offers to get some bait and some sardines for the old man. The boy helps Santiago carry his gear to his shack, they discuss baseball and the lottery, and then the boy brings him food. In the morning, before they leave for fishing, they have coffee together. Hemingway spends all that time on establishing the profound relationship between the old man and the boy because it is crucial to what happens at the end of the novella.
After the old man's tremendous battle with the great marlin, he returns to the village late at night when everyone else is asleep, pulls the boat ashore, carries his mast and sail to his shack, and falls asleep. That's where the boy finds him in the morning. He has seen the gigantic skeleton of the marlin lashed to the side of Santiago's boat and realizes the ordeal the old man must have gone through. The boy weeps in sympathy at the old man's injuries but also out of happiness that at least he is alive. When the boy brings hot coffee to the old man and they converse, the boy says that he will start going fishing with Santiago again because he still has a lot to learn. When Santiago says he is unlucky, the boy says, "To hell with luck. I'll bring the luck with me." They make plans together for their partnership, and the boy says he will bring some food and some medicine for Santiago's hands. As the boy leaves, he is weeping again, but this time it is out of relief that the old man is all right and that they will be partners again.
We see, then, that the boy thinks that the accomplishment was worth the price because it will allow him and the old man to work together again. He comforts Santiago materially with coffee, food, and medicine, and he also comforts him with the reassurance that he plans to accompany him again. Deep within himself the boy feels a bond of love and respect for the old man.