Tobias is a show-off. He believes that he is a heavily built jock, but in reality, he is not. Despite him not having a good athletic build, he is obsessed with sports, and is always trying to hone his scrawny physique. He also seems to have a very big ego.
Because of his inflated ego, Tobias is more confident in his abilities to court Penny than Gumball is. Tobias can also be somewhat of a bully sometimes, such as when he was tossing Anais' plush Daisy doll around on the bus, and seemed quite eager to hurt Gumball in "The Knights." Also, in "The Robot," he insults Bobert, calling him "Robo-dork" and commenting on his apparent lack of feelings. Also in "The Uploads," Tobias found it funny when his father got hurt from falling off a skateboard that he placed in front of a staircase for a prank. In "The One," it is shown that because of Tobias's narcissism he does not understand true friendship. He tries to insert himself into Gumball's life, and tries to eliminate Gumball's other friends (including Darwin), so he can be his only friend. He seems to realize the error of his ways after Gumball sets him straight.
Tobias also seems to be quite the womanizer. He is very quick to make moves on every girl he sees (his father displayed similar behavior at his age in "The Choices" when talking to Nicole at a younger age.) Despite all of these girls showing disgust toward Tobias' advances, he still continues to pursue these girls in hopes of one day having someone further inflate his ego and "macho" antics.
According to Alan in "The Third," Tobias comes from a wealthier household than most of his classmates. More proof of Tobias's wealth is shown in the episode "The Candidate" where his parents funded a significant part of the books, food, etc.