Steinbeck incorporates much in way of the opening exchange between both men to help us understand the nature of their relationship. One significant inclusion is that George is the "brains" of the operation. This is seen at different points in the opening exchange. George's opening reprimand of Lennie to not "drink so much" water is one such moment. When he gets angry at Lennie for the dead mouse, it is another example of the control that George has in the relationship. Finally, when George instructs Lennie to "say nothing" it is a telling moment in which one sees that he is the "brains" of the outfit. This is something that will dominate the narrative.
I think that another dynamic of their relationship is one where George recognizes his own anger. This comes at a particularly poignant moment in the exchange when, after George yells at Lennie stemming from his request of ketchup, George concedes that "I been mean, ain't I?" This moment of recognition and the contrition that follows is reflective of how George cares for Lennie and does look out for him. This is seen in the ending when, in their final exchange, George tells Lennie, "I ain't mad at you." This is right before he has to commit the ultimate act of care for Lennie.
Finally, I think that George's mention of Aunt Clara reflects how he feels bound to Lennie out of a promise made to the woman. While Lennie does trouble George and while George yells at him often, the reality is that George feels a sense of obligations and duty towards Lennie. Out of the promise made to Aunt Clara, something seen in full in chapter 6, George cares for Lennie. In these moments, the telling aspects of their relationship emerge in Chapter 1 and will be evident as the narrative develops.