When he's not Spiderman, he's Morgan Stark's older "brother". After Tony died, Peter felt it was his duty and obligation to watch Morgan grow up and be the male figure missing from her life. Although he wasn't totally raising her, since she still had Pepper, he still felt the need to fill Tony's shoes as best as he could. Keeping a little girl happy is hard, but it's a hero's duty to keep the citizens happy and safe, and that includes your little sister.