I think that one reason why Lennie imitates George's movements is because he looks up to him. Lennie recognizes that George operates as sort of the "brains behind the operation." George constantly tends to Lennie and looks out for him. Lennie sees George in a position of leadership. It is for this reason that he imitates George. Whether it's how he sits or how he wears his hat, George occupies a place of importance and stature in Lennie's mind.
This also tells us how much Lennie shows deference to George. Lennie recognizes that George is the only person who would "give a hoot in hell" about him. In imitating him, it is clear that Lennie knows that George is where power lies. In imitating him, Lennie learns how to act and how he is to behave. Since he follows George's instructions, for the most part, without hesitation, imitating him is another way that the bond between them is strengthened. This ends up becoming part of the reason why he continues to imitate George.