Why should David not put Naval's words to heart?
Malbim: Disgrace is only from an honored person, between equals, but not from a lowly, disgraced person. People are not concerned for his disgrace. 1 He always does so!
Rashi (Kesuvos 40a): A lowly person who shamed someone pays less than an average person. However, the Yerushalmi (Kesuvos 3:8) and the Rambam (Hilchos Chovel u'Mazik 3:1) say that a lowly person pays more! Did Avigayil say so merely to placate David, but it is not true? (PF)
Why did she say both "let your slave speak in your ears, and hear the words of your slave"?
Kli Yakar: Aloud, I will say for all to hear [that you are justified to kill out Naval's house]. There is a secret to say only in your ears [that I am not guilty, for I did not know about your youths].
