It's tough to be Sonya. Like Yelena, she's a woman (well, obviously). Now, in the world of Uncle Vanya, this means that even if she has some smarts, power, and a good work ethic, she's still pretty much made to do one thing and one thing only: marry somebody.
The problem with Sonya, though, is that she's not that cute. This point comes up over and over again in the play, showing how superficial everyone's opinion of the young lady is. It's the first and most important thing everyone notices. We know that she's really hard working, based on the way that her uncle Vanya talks about her:
VOYNITSKY: [...] I used to not have a spare minute, Sonya and I worked – my goodness, how we worked, and now only Sonya works and I sleep, eat and drink… That's no good! (1.62-65)
Sonya is the only one who's impervious (there's a ten-dollar word for you) to the arrival of her father and Yelena. Everyone else complains about the way that the couple have screwed up the estate's schedule, but she just keeps her nose to the grindstone.
Unfortunately, good qualities like that one don't do much for her in the marriage-crazy society she lives in. Her problem is that she's "plain," which is basically a code word for ugly or, at least, not very pretty. And, unfortunately, Sonya knows that she's plain. And, even more unfortunately, it really gets to her.
SONYA: [Wringing her hands.] Oh how I hate being plain! It's dreadful! And I know I'm plain, I know it, I know it… Last Sunday when we were leaving church, I heard people talking about me and one woman said, 'She's kind and generous, but it's a pity that she's so plain.' Plain… (2.380-84)
Sonya, because she's so good (generous, kind, hard-working…) is pretty useful for revealing the hypocrisy of the society she lives in. Like those old ladies dishing about her at church: they'd so much rather have someone who is beautiful than someone who is good.
The fact that this particular event happened at church, where you might expect people to look for inner beauty, shows that even the best virtues can't compete with a pretty face or a smokin' bod. This falseness is kind of like the falseness of Serebryakov, who lives off money that isn't his. In both cases, appearances are worth more than reality.
Now, we know that most characters in this play don't get what they want. But in Sonya's case, this lack of fulfillment is especially cruel, since the main thing preventing her from finding what she wants (in her case, love) is that she just isn't that hot. Unlike Vanya, who is pretty lazy, or Yelena, who causes people a lot of trouble (even if unintentionally), Sonya really doesn't do anything wrong; she just happened to be born plain.
Though we can find fault with some of what she does (see below), the root of her problem, at least initially, is beyond her control. Through Sonya, Chekhov is showing us that when it comes right down to it, life just isn't fair.
Sonya is pretty much the only character in the whole play who keeps her head (even if she does go a little bit gaga for Astrov) and tries to get everyone else to follow suit. She's always running around playing peacemaker, begging her uncle to simmer down and quit insulting her dad, begging Astrov to quit getting drunk, and begging her dad to just be nice.
It seems noble, right? But it's also one way that Sonya just completely loses herself, to her own detriment. She doesn't fight for her rights to the estate when her dad tries to sell it, and she doesn't share her emotions with Astrov until Yelena pretty much strong-arms her into doing it. (Even then, she relies on Yelena to make the move.) She's so peaceful that she tiptoes herself right into a forgotten corner, where no one thinks to help her.
What holds back Sonya from making any kind of splash isn't nobility; it's fear. And her fear is the one that keeps everyone, Vanya, Yelena, even Marina, down in the play. It's fear of facing the truth.
When Yelena and Sonya plot to find out whether Astrov has feelings for the girl, Yelena is sure that knowing will relieve Sonya's mind:
SONYA: [in great agitation] You will tell me the whole truth, won't you?
YELENA ANDREYEVNA: Yes, of course. I think that the truth, whatever it is, is not as frightening as uncertainty. Rely on me, my dear.
SONYA: Yes… yes… I'll say that you want to see his plans… [Goes and stops by the door.] No, uncertainty is better… There's still hope… (3.98-105)
See what we're saying? Sonya has a little bit of a desire to know the truth, but she changes her mind about it. She thinks that as long as she has the uncertainty, there's still a chance that the Doctor will say yes.
Of course, not knowing doesn't improve her chances at all; it just keeps her in the dark. Sonya's in denial.
And that denial is what lets everyone in the play ignore the problems swirling around them and just go on with their lives. It's like they've got blinders on, ignoring the fact that their estate is going to pot, that their crushes don't feel the same way they do, and that they're all going to be miserable for the rest of their lives.