The word "Ki" seems to have different meanings in the same Pasuk!
Rashi and Rashbam: The first "Ki" in the Pasuk means 'because' ("because she was afraid"), whereas the second one means 'but' ("but you did laugh"). In fact, 'Ki' has two other connotations as well - Iy or Asher ('if,' or 'when') and 'Dilma' (perhaps). 1
Riva: The Targum of [almost] every Ki is 'Arei,' for Arei has these four meanings in Aramaic.
Why did Sarah deny that she laughed even after Avraham had rebuked her, ostensibly in the name of HaSh-m?
Ramban: Avraham did not quote HaSh-m; so she thought that he was taking her to task off his own bat. Perhaps he had seen some giveaway sign on her face, or because she had failed to acknowledge the good news. The moment he said to her, 'No, but you did laugh!,' she realized that he had spoken prophetically, and she stopped denying.
Why does it say "and Sarah denied" (rather than simply, 'she said')?
Hadar Zekenim: This shows that women deny.
