When we take a look at Tomas's character, we find that he is a great jumping off point for discussions of es muss sein and einmal ist keinmal. Similarly, Tereza is our gateway to Kundera's discussion of the body/soul dichotomy. As the narrator says: "[Characters are] not born of a mother's womb; they [are] born of a stimulating phrase or two […]. Tereza was born of the rumbling of a stomach" (2.1.1).
We know that Tereza has some serious body issues. Go ahead and re-read the first few chapters of Part 2, in which the narrator tells us about Tereza's childhood and relationship with her mother. As a young girl, Tereza was never allowed any privacy, nor any sense of shame with regard to her body. Her mother paraded around her own nudity and physicality, and tried to force Tereza to do the same. In Tereza's mind, this violation of privacy was akin to a concentration camp. She learned to hate the body, and so she identified herself with the soul hidden within it.
A long time ago, says the narrator, people used to think of the self this way. The body was a cage, and the soul was trapped inside it. But in the modern day, we don't think this way anymore. Because of science, we know that "the soul is nothing more than the gray matter of the brain in action. The old duality of body and soul has become shrouded in scientific terminology, and we can laugh at it as merely an obsolete prejudice" (2.2.4).
This is where Tereza's anachronistic (i.e., old fashioned) nature comes into the picture. She still thinks about the soul and body the way people used to back in the day. In her mind, the body and soul are completely separate and irreconcilable. This incompatibility is evident in the rumbling of the stomach that inspired her character. Look at it this way: Tereza shows up at Tomas's place in Prague, in love with him, offering up her life – her soul – to him. And then her stomach rumbles. The gross physicality of her body is a thing completely separate from the purity of her soul. In a moment as important as falling in love, her body is still just a body going through its body motions. As the narrator says, this moment "brutally reveals the irreconcilable duality of body and soul, that fundamental human experience" (2.2.1).
This is part of the reason that Tomas's infidelities weigh so heavily on Tereza.:
She had come to him to escape her mother's world, a world where all bodies were equal. She had come to him to make her body unique, irreplaceable. But he, too, had drawn an equal sign between her and the rest of them: he kissed them all alike, stroked them alike, made no, absolutely no distinction between Tereza's body and the other bodies. He had sent her back into the world she tried to escape, sent her to march naked with the other naked women. (2.15.7)
Take a look at the series of dreams that haunt Tereza in the novel – they all have their roots in her traumatic childhood, her body issues, and this duality of body and soul.
The connection to lightness and weight comes in naturally when you pair up the two dichotomies (i.e., light and darkness, soul and body). The body is paired with lightness, while the soul is paired with weight. Tereza's desire to find herself in her soul is fitting given her association with weight – think about the heavy suitcase she brings with her to Prague. Similarly, her desire to dismiss her body goes hand-in-hand with her inability to embrace lightness.
The two come together nicely in the episode with the engineer. Tereza decides to give living lightly a shot, and so sends her body out into the world, or rather, into the arms of the engineer she meets at the bar. You know how the story goes from there, and the narrator takes a close look at the outcome: "Did her adventure with the engineer teach her that casual sex has nothing to do with love?" he asks. "That it is light, weightless? Was she calmer now?" (4.21.2). And then he answers: "Not in the least" (4.21.3).
What we see is that Tereza – just like Tomas – has failed to embrace and rejoice in lightness. In a very different way, and in a very different character, the narrator has demonstrated once again that the lightness of being is, in fact, unbearable.