I think what is most remarkable about Oskar is that while he is clearly depressed by his father's death, the state of his family, and many other woes, and he acknowledges the many ideas and hardships that give him "heavy boots" he is never defeated by the "heavy boots." He has an amazing resiliency to the difficulties in life. He is single-minded in his determination to find the lock for the mysterious key. He thinks about things over and over until he understands them or at least until he can deal with them. He has such a powerful, positive influence on those around him, that I think we have to say that the "heavy boots" create a very bittersweet little boy who is wise beyond his years and ends up OK in the end.
Oscar bruises himself when he has heavy boots (feeling depressed); he often does this after a day of unprogressive searching for the Blacks.
He also tries to invente someting that could solve the cause to the problem he's facing; like a elevator so the floor comes to you, so incase of a fire everyone will be safe.
Thirdly, he tries to be funny, and tells jokes; like in the limo on his way to his father's funeral.