Parshas Chayei Sarah
I would suggest that the lesson is in the way in which Sarah died. The messenger paused, and in that moment Sarah expired from the shock.
Parshas Vayeira
The Gemara in Bava Kamma explains that Ammon was rewarded for the more refined language of their matriarch.
In the introduction to Sefer Chovas Hashmira, the Chofetz Chaim derives from this Gemara that even the speech of non-Jews, who have no mitzvah to speak nicely, is noticed and rewarded by Hashem.
Parshas Lech Lecha
In Sefer K’vod Shomayim, the Chofetz Chaim urges the reader to consider the immense reward which comes to one who chooses silence instead of causing problems through speech. As proof, he points to Lot, the nephew and erstwhile traveling companion of Avraham Avinu.
Parshas Noach
The Chofetz Chaim points out in Shemiras Halashon that Cham is severely punished for revealing Noach’s state; his intention was not to alert his brothers so they could act to preserve Noach’s dignity, but rather to have a laugh at their father’s expense.
Parshas Beraishis
In other words, the defining feature which distinguishes people from all other of Hashem’s creations, is the power of speech.