Right from the get-go, it’s clear that George Tesman comes from a class below Hedda. Where she is formal and reserved, he is casual and open. At the least, he’s unsophisticated or, as Brack refers to him, "a simple soul."
Unfortunately for George, Hedda resents him for their class difference – something he can do nothing about. The big tip-off comes when she says, "with a touch of scorn," "Tesman always goes around worrying about how people are going to make a living." If he were an aristocrat, money wouldn’t be an issue. He wouldn’t HAVE to worry about it. (This cavalier attitude is Hedda’s approach to wealth, if you hadn’t noticed.)
But in Hedda’s eyes, George fails in more ways than one. Compare his professional life to that of Eilert. Eilert is creative, productive, daring; he’s just written two books, one incredibly controversial. When Tesman remarks that "It would never have occurred to [him] to write about anything like that," Hedda pointedly replies, "Of course not." George doesn’t create; he can only immerse himself in other people’s work. That’s why his defining prop (see "Tools of Characterization" for more) is a suitcase full of notes or a stack of books. "Setting other people’s papers in order [is] exactly what I can do best," he says. And he’s right.
Then there’s the social stuff. George just follows the rules without question. He makes a big deal out of Hedda having a chaperone if she’s going to sit with Eilert. In Act IV, when he first hears that Hedda has burned the manuscript, his response is, "It’s illegal disposition of lost property!"
Which brings us to our next point. George rejoices in Hedda’s destroying the manuscript, rather than condemning her for ruining a man’s life work (and probably his life, as far as George knows at this point). This isn’t the only instance of George being on shaky moral ground because of Hedda. In Act I, George isn’t the least bit embarrassed about the shame his wife causes Aunt Julie. When Miss Tesman says that she bought the hat for Hedda’s sake, so that "Hedda wouldn’t feel ashamed of [her] if [they] walked down the street together," George responds not with outrage or reassurances or apologies, but rather, "You think of everything, Aunt Julie!" He’s so blinded by sheer adoration of his wife that he doesn’t consider the destructive effect she’s having on those around her.
Notice that we said "adoration" for his wife – not love. We can’t be sure exactly how George feels about Hedda, because, honestly, he’s too star-struck to deal with her as a real person. He loves to "wait on her," he does everything she says without complaint, and he’s constantly congratulating himself for marrying the most eligible bachelorette in town. "I rather suspect I have several friends who’d like to trade places with me," he says. George doesn’t even know who Hedda really is – that’s clear from the scene in Act IV when he buys her story about why she burned the manuscript. If he only knew what was going on in that head of hers…