In addition to studying the black culture of the day, you would probably find a look at the Jewish cultural position quite enlightening. The prejudices and cruelties perpetrated against blacks are well documented; not so with the Jewish culture, and this book clearly indicates that it existed.
One option if you would rather not bring in additional sources is to focus on the importance of experiences in shaping people's lives. Perhaps you could look at the author's experiences and how it may have shaped who he is; you could also take it a step further if you want by comparing his experiences and how they influenced him to his mother's experiences and how they influenced he
I LOVE, love, love this book, first of all. Have you read it yet? It is a wonderful memoir and truly eye-opening.
An obvious idea for a thesis paper would be to deal with some aspect of African-American culture/race vs. Caucasian, since his mother was white and his father was black. You might want to explore that. You could actually tie his own experience to Barack Obama's experience, since his mother was also white and his father was black. Both the author of The Color of Water and Barack Obama went through very similar experiences growing up. Whether or not you agree with Obama's politics, the comparison would be fascinating. A good start would be to read Barack Obama's biography called Dreams from my Father.