Quote 1
"Maybe the two different worlds we live in weren't so different. We saw the same sunset." (3.18)
Cherry Valance gets Pony thinking about nature – something he already loves – as a connecting factor that doesn't care about class or wealth.
Quote 2
"Ponyboy… I mean… if I see you in the hall at school or something and so hi, well it's not personal or anything, but…[…] We couldn't let our parents see us with you all. You're a nice boy and everything…" (3.62)
Ouch! Cherry's comment shows just how committed she is to the rules and norms of her social circles, from peers to parents. It also suggests she's under lots and lots of pressure to be loyal to her group and conform to those rules, even as she wants to break them.
Quote 3
"I could fall in love with Dallas Winston. […] I hope I never see him again or I will." (3.65)
Cherry likes dangerous, violent, good-looking guys, regardless of how much money they have. Why do you think she shares this info with Pony, and how might it make him feel?