The first piece of content from J.K. Rowling in the early chapters of
Harry Potter and the Deathly Hallows was released on Pottermore this Tuesday, giving a bit more insight into the relationship between Petunia and Vernon Dursley. Rowling's thoughts on the couple and how their names came about, and even that glimmer of hope with Petunia in the third chapter of the final book, can be read here.
Quote:
J.K. Rowling: The Dursleys are reactionary, prejudiced, narrow-minded, ignorant and bigoted; most of my least favourite things. I wanted to suggest, in the final book, that something decent (a long-forgotten but dimly burning love of her sister; the realisation that she might never see Lily's eyes again) almost struggled out of Aunt Petunia when she said goodbye to Harry for the last time, but that she is not able to admit to it, or show those long-buried feelings. Although some readers wanted more from Aunt Petunia during this farewell, I still think that I have her behave in a way that is most consistent with her thoughts and feelings throughout the previous seven books.
Nobody ever seemed to expect any better from Uncle Vernon, so they were not disappointed.
More tidbits from Rowling in
Deathly Hallows, including how Extension Charms ('Capacious Extremis!') work, the Sword of Gryffindor's history (which she does liken to King Arthur's Excalibur), Alchemy, and more.
J.K. Rowling explains Petunia Dursley's almost farewell to Harry in 'Deathly Hallows' 
