Theo's the kind of person who gives his half of the $10,000 to his parents. Who does that? Think about it: that's a pretty rare quality. When we first meet Theo, he's a high school senior, and a little bit in Doug Hoo's shadow. While he has his own ambitions to be a writer and get a higher education, Theo is almost too willing to sacrifice those things for his family. Even though he has a partial scholarship to a university, he's going to walk away so his family has enough money to take care of his brother's medical needs. When he unconsciously defines himself as a brother first, he has to pause to think about what that really means; while he might resent it a little, he can't be too upset when he compares himself to how his brother Chris conducts himself with such a pure spirit in a really tough situation.
Theo's also one of the few characters who likes to play chess, and one of the few to go up against Sam Westing, even though he doesn't know that's what he's doing. He has a lot of initiative when it comes to playing the Westing game, although his partner Doug's not much help. He's one of the first people to suggest they should all share their individual clues, and when he's working on his own, he comes up with a scientific formula. Now, he also comes up with clues that point to Otis, and while he's not above spying on Otis to see if he really is the murderer, he has the good sense to be ashamed when all he finds out is that Otis is a regular volunteer at the soup kitchen.
At the end of the book, we see Theo accomplish his desires: he studies journalism at university and becomes a novelist. While he's not very successful, he gets to pursue what he loves. He's married to Turtle, even though he spent most of the Westing game with a crush on her older sister. They've decided not to have children; although they'd both like them, they don't want to take the chance of giving someone else Chris's disease. That's Theo: responsible and always thinking of others first.