The quote appears in Book IV, Chapter IV. In this chapter Jim and Antonia are reunited. So much has happened to each of them: Jim has attended law school, and Antonia has been jilted by her fiance and left with a baby. Nevertheless, the pair are so happy to see each other; even though their lives have changed so much, there is a deep truth that each finds in the other that is changeless. They love each other, but in a way that perhaps transcends romantic love -- it is the love that comes from being fully known.
When Jim says to her, "Do you know, Ántonia, since I’ve been away, I think of you more often than of any one else in this part of the world. I’d have liked to have you for a sweetheart, or a wife, or my mother or my sister — anything that a woman can be to a man. The idea of you is a part of my mind; you influence my likes and dislikes, all my tastes, hundreds of times when I don’t realize it. You really are a part of me,” he is finally expressing his pent up feelings; but Antonia, always somehow unattainable, just says "Ain’t it wonderful, Jim, how much people can mean to each other? I’m so glad we had each other when we were little." There is a bittersweet quality to this moment -- she is not exactly refusing him, although it must feel a little that way for Jim. It is more an affirmation of what they do share, which is the past, a past that stretches into the future.
The quote in question is an interesting twist on this theme. If Jim is expressing his long suppressed feelings for Antonia, the quote seems to suggest that Antonia might think of Jim, with his Harvard education, as equally unattainable. When she says that "even the happiest" people think about the old times, she is making a sly reference to Jim himself, as if she is imagining him back east practicing law, living a very different life, happy and separate.
I don't think Antonia envies Jim. Her greatest quality is her complete lack of self pity or envy. Instead, the chapter ends with an affirmation of what they share. As Jim says, as he returned to the Widow Steaven's place afterward:
As I went back alone over that familiar road, I could almost believe that a boy and girl ran along beside me, as our shadows used to do, laughing and whispering to each other in the grass.