I would say that Finny is a static character. At the beginning of the novel, Finny is a completely altruistic character. He loves life. He enjoys being around friends, enjoys athletics, is spontaneous, friendly, and quite charismatic. Gene, the narrator, seems to refer to Finny with almost Greek god-like characteristics. Finny is near perfect in athletic ability and personality. Gene assumes that because he is jealous of Finny's athletic prowess that Finny must be equally jealous of Gene's academic abilities. It's a tough lesson for Gene when he learns that Finny doesn't care and genuinely wants to see Gene succeed. Finny absolutely sees the best in people all of the time and wants what's best for other people all of the time.
That assumption in the general goodness of people does not change through the novel. Gene confesses to Finny twice that he shook the branch intentionally that caused the leg break. Finny doesn't believe it and basically tells Gene that he won't hear of it anymore. Finny continues to help Gene with athletics and they hang out together all of the time. Despite his leg injury ending any chance at athletics Finny still love life. He is still optimistic, spontaneous, and as charismatic as ever.
Even at the end of the novel when the "trial" forces him to really look at the facts, he refuses to hear of it and leaves.