The Question and Answer section for The Lightning Thief is a great resource to ask questions, find answers, and discuss the novel.
Grover was bullied because he was different, and his differences made it easy for other kids to bully him. He was scrawny, emotional, cripple (a muscular disease in his legs), and he walked funny.
What chapter are you referring to?
Percy left Grover by the bus station and Grover was charged with looking after Percy.