Kenny is on shaky social ground himself, and is afraid that if he associates with Rufus, he will be teased all the more.
Kenny is not "cool" like his brother Byron; he is "just another fourth-grade punk". There are two things "wrong" with Kenny that make the other kids want to give him a hard time - he loves to read, and he has a lazy eye (Ch.2).
When Rufus shows up, Kenny is relieved because he thinks that now the kids will now tease the "new kid" instead of him. He is appalled when the teacher seats the boy next to him, because,
"when you (have) two people who (are) going to get teased a lot and they (are) close together people (don't) choose one of them to tease, they (pick) on both of them, and instead of picking on them the normal amount they (pick) on them twice as much".
Kenny is wrong in his calculations, however. He and Rufus become good friends, and Kenny is dismayed when he realizes that the kids actually do start "leaving (him) alone and going right after Rufus" instead. Rufus has two things wrong with him too - his "countrified" background and poverty, as evidenced by his clothes. Kenny feels "real bad" about his new friend's situation, but nevertheless hurts Rufus's feelings deeply one day when he joins in the other kids' teasing. With Momma's help, he apologizes to Rufus and makes things right, learning a valuable lesson about the nature of friendship (Ch.3).