George and Lennie's relationship appears to be one-sided, all 'give' on Georges' side and 'take' on Lennie's. Examine it closely to discover what aspects of it give it more balance than appears on the surface.
One point in the story where Lennie's value and tenacity as a friend is expressed is the section set in Crooks' room. There Lennie gets angry with Crooks and clearly defines his role as George's protector (if George were to ever need one).
This is a small token, perhaps, but it is one more proof that the relationship is not completely unbalanced.
Caring for Lennie is important to George. I will add to the excellent and detailed responses of the other posters. We get some satisfaction from being selfless, the martyr's satisfaction. This is part of what it is for George. He has to take care of Lennie because that is the role he has set for himself, no matter what suffering ensues.
Having read the novella, if you will reread the first chapter you will better perceive the interplay of George and Lennie. One perception may be a realization that while the anthropomorphic qualities of Lennie--his "paws" and his dragging feet and hanging arms--suggest a dumb brute, but Lennie plays a very significant role as the keeper of the Dream. With his child-like innocence, Lennie insists upon hearing about the dream of the ranch as a child enjoys his favorite fairy tale. And, after so many recitations, George begins to believe that owning a piece of land may actually be a possibility. This recitation of the dream becomes an incantation for not only George and Lennie, but the old despairing Candy, who finds new hope; even Crooks awakens to the possibility that there may be a life yet for him.
Then, too, Lenny protects George physically. When Curley enters the bunkhouse and becomes belligerent after Slim derides him, he looks at the small George and bypasses him, knowing that Lennie would protect George if he were to hit him. Since this would make two against one for Curley, so he avoids George.
Finally, there is a real frienship between George and Lennie. After bemoaning the trouble it is to go around with Lennie--
I could get along so easy and so nice if I didn't have you on my tail. I could live so easy and maybe have a girl--
George is ashamed and later recites,
With us it ain't like that. We got a future. We got somebody to talk to that gives a damn about us. We don't have to sit in no bar room blowin' in our jack jus' because we got no place else to go. If them other guys gets in jail they can rot for all anybody gives a damn. But not us.
Lennie breaks in and fininshes,
But not us! An' why? Because...because I got you to look after me, and you got me to look after you, and that's why. (Chapter One)
When Lennie dies, the Dream dies and George is absolutely alone and without hope.
Steinbeck seems to go to great length to develop the typical lifestyle of the itinerent farm laborer during the Great Depression in central California. He particularly portrays this through the characters of George and Lennie as they value each other's friendship. Furthermore, he demonstrates their individually develops their characters so readers understand two different archetypical characters from the era.
Although George and Lennie's relationship appears one-sided, it is not. George receives the love and affection from Lennie an owner might receive from its dog, or a father might receive from a son. Lennie looks forward to spending time with George. When Crooks suggests George might forever leave Lennie in chapter 4, Lennie is devastated by the idea and enraged at the suggestion. This proves Lennie's familial need for George, not to mention the fact that he cannot take care of himself by himself. Although George likes to make it seem like Lennie is a pain to have around, Lennie actually gives George something to be responsible for. This might be an aspect of life George would have lacked without Lennie. George might have just blown his money all the time at places like Susy's if it hadn't been for Lennie.
These should be some ideas that help you see your prompt both ways.