Ultimately, no intimacy
I watched it again tonight for the 100th time over the years. But this time something different struck me. Connie and Edward have nothing to say to each other. It's not familiarity from living together for so long, it's not a fun comfortableness. They don't communicate at all. The scene when Edward says "Do you love me, Connie?" And she says, "Of course I do." There is nothing else. No..."Why do you ask?" Nothing. I know she feels guilty and distracted, but there isn't any impulse in either of them to inquire about the other in a meaningful way. Even at the beginning, they joked around (sort of) but there was no genuine connecting. Ironically, Connie opened up more (no pun) w/ Paul, even revealing to him how much she obsessed about him. That lack of intimacy was solved during her dalliances w/ Paul. He gave her everything she was missing, especially playful and "naughty" sex. No shame and no inhibitions, unlike w/ Edward.
We see her crying when she finds out he is dead. She doesn't even attempt to conceal it from Edward. I think she was crying because it's over and he's gone permanently. Despite herself, she was in love w/ him.