When we first see Sophia Western, the narrator comes out and tells us that she is our heroine. Not only is she Tom's love interest, but she is also beautiful, graceful, and talented in her own right. In fact, the narrator dedicates most of the chapter that introduces her to coming up with outlandish and poetic descriptions of her beauty and sweetness of temper.
Still, the main core of her characterization is that she is in love with Tom. She's introduced in Book 4, Chapter 2, and her feelings for Tom come up in Book 4, Chapter 3. Clearly, Sophia's deep appreciation for Tom's "gaiety of […] temper" (4.3.4) is what makes her our central heroine. The thing is, as Mr. Blifil admits, Sophia is extremely marriageable. She is wealthy and gorgeous, so of course she would be a huge catch for Tom, and his marriage to her is like the final proof of his rise to worldly success.
Yet, even if Sophia is mostly involved in the novel because of her attachment to Tom (and Tom's attachment to her), she does develop as a character over the course of the book. Sophia's struggles give Fielding a chance to think about the limits of parental authority.
The thing is, Squire Western has the power to force Sophia to marry someone she despises, Mr. Blifil. But just because the squire has that power doesn't mean that he should exercise it. Squire Allworthy is the voice of reason during all of this, since he keeps preaching that Squire Western shouldn't use violence to force Sophia to act against her will.
But there is no legal reason why a father can't force his daughter to marry in this place and time. And while Fielding doesn't generally seem like much of a feminist (since the whole purpose of Sophia's character is to dodge marriage with unsuitable men until she can wind up hitched to Tom), he does suggest that it's unfair that fathers have so much legal authority over their children.
Sophia has to spend most of the novel wrestling against the social idea that women should be obedient to their fathers. But she does it in this kind of cool way. Well, first she "argues" by running away with her maid, Mrs. Honour, to say with her relative, Lady Bellaston, in London. Absence is actually a pretty strong argument. It's not like Squire Western can make her do anything when she isn't even in Somerset.
But before Sophia leaves home and after she meets Squire and Mrs. Western in London, she tries to reason with her family. She points out that she hates Mr. Blifil, but Mrs. Western doesn't see this as a problem—it's fashionable in London to hate your husband. Sophia also notes (pretty brilliantly, we think) that she would never marry a man her father disapproves of. So shouldn't he do her the same courtesy of not marrying her to a man of whom she disapproves? (Squire Western refuses to listen to this logic, but we think it makes sense.)
Sophia proposes a different model of authority, where father-child relations are less a matter of the dad dictating what's going to happen to the child, and more an equal exchange of respect and care. Sophia asks her father to trust her to be a good daughter, just as she relies on him to be her dad. It's surprising how many fathers in this book don't want to go along with a deal that seems fair enough to us. There are a surprising number of bossy, tyrannical dads in this book, who really want their children to behave basically as extensions of their own wishes.
There's Squire Western, obviously, but Nightingale Senior also tries to arrange his son's marriage to a wealthy but unpleasant young woman. But the book clearly disapproves of these fathers: Squire Allworthy is the real model parent here. He's willing to let kids have their own choice of what they do (as long as they live according to a strong moral code of honor).
Clearly, Fielding is trying to suggest a moderate course for parental authority: a father should guide his kids' behavior with lessons about right and wrong, but he shouldn't try to squelch his kids' individuality or personal choice. Kids aren't clones of their parents, as Sophia knows but as Squire Western never really learns.
By the end of the novel, Sophia has repeated over and over again to her father that she isn't trying to hurt him by refusing to marry Mr. Blifil. She just thinks that it's wrong for her to marry a man she despises. She swears that she won't marry a man of whom her father disapproves (*ahem*Tom*ahem*), but she also can't get hitched to a fellow of whom she disapproves. All her father sees is Sophia's disobedience. But in Sophia's eyes, she is doing her best to respect her father's wishes. She doesn't elope with Tom, after all, even before Tom manages to make her mad by sleeping with Mrs. Waters at the inn at Upton.
In a way, this argument between Sophia and Squire Western never really gets resolved. Both of them reach this unmovable decision: Sophia will not marry Mr. Blifil, and Squire Western insists that she will. There is no compromise here, and both of them build up a lot of resentment, anger, and genuine pain towards the other for hurting their feelings so badly.
What changes things between father and daughter is that Tom changes: he becomes Squire Allworthy's heir, and thus marriageable. Squire Western suddenly becomes Tom's biggest fan. While Sophia still resists Tom briefly (thanks to his many infidelities), it's Squire Western who steps in and complains:
"[…] thou dost love to be disobedient, and to plague and vex thy father […] When I forbid her, then it was all nothing but sighing and whining, and languishing and writing; now I am for thee, she is against thee. All the spirit of contrary, that's all." (18.12.8)
Sophia finally agrees to marry Tom the next day, as her father wishes. But he is right that Sophia's sudden obedience is rather out of character, even though she so often talks a good game about the importance of listening to her dad. Sophia obeys her father when it suits her, and refuses (even though it pains her) when she can't. What would you say the book's final message is about children and obedience? If Tom hadn't suddenly become Somerset's most eligible bachelor, what would Sophia have done?