Occasionally, George tells Lennie that he would be better off alone and that Lennie is holding him back. "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." However, George stays with Lennie because he feels obligated to look after him, because he knows that Lennie needs him, and because the life of an itinerant rancher is a lonely one. It's better to have someone than to be alone.
When their new boss questions them, George lies and says Lennie was kicked by a horse. He does this to stop the interrogation. But George seems to trust Slim almost immediately. When Slim asks if they travel together, George replies that he and Lennie "kinda look after each other."
In Chapter 3, Slim notes that it is odd that George and Lennie travel together. He says this because most workers live alone, traveling from job to job. Slim says, "You know how the hands are, they just come in and get their bunk and work a month, and then they quit and go out alone." This shows what a lonely life a traveling ranch hand can be. This is one of the reasons George and Lennie stay together: to avoid being alone.
George opens up to Slim here and tells him how he came to look after Lennie.
I knowed his Aunt Clara. She took him when he was a baby and raised him up. When his Aunt Clara died, Lennie just come along with me out workin'. Got kinda used to each other after a little while.
It is likely that George feels obligated to watch Lennie, perhaps from some promise he may have made to Aunt Clara. But he also grows accustomed to having Lennie around and George realizes that Lennie would be lost without him.