Lord Wessex is William Shakespeare's opposite in almost every way. He's humorless. He's dumpy (only this film could make Colin Firth look dumpy.) He's a jerk. And Viola simply doesn't love him.
Wessex is insecure because he is a man with a title but no money (okay, that's one way he is similar to Will, who has no title and no money), and to get money, Wessex makes a bargain with Viola's father, trading parts of his tobacco plantations for her hand in marriage. Buying a woman who doesn't want to marry him automatically makes him a cad. In case you weren't certain he's a jerk, he tells her,
"Be submissive, modest, grateful and brief."
Wessex also is clumsy with words. Shakespeare writes sonnets about Viola's beauty, but when Viola asks Wessex why he is attracted to her, he can barely answer: "It was your eyes. No, your lips." He's not a poet and he knows it.
One dramatic moment occurs when Wessex and Shakespeare. Shakespeare would have killed him, but the sword he stabs him with turns out to be a fake prop sword. How do you think Viola would have reacted if Will did kill him? It's unlikely she would have mourned Wessex's death, but would it have changed her opinion about her lover?
In the end, Wessex doesn't have to change his ways because he is an upper-class man and he gets what he wants. Viola must go to America with him, on orders from the Queen. Shakespeare is a low-class playwright, and he stands no chance against Wessex. But the proof that his own wife doesn't love him will likely keep Wessex an insecure little troll for a long, long time.