>>114068170I'll take a crack at it: Karen already connects really well with three of the five girls. She attends green/peace rallies with Jess when no one else will; she geeks out with Babs on pop geek shows and gadget tech and then there's Zee.
Karen is one of two people who gives Zee true admiration. She legit completely believes in Zee in a time where Zee needs this reassurance the most (Zee breaking away from her father and starting out; insecurity about her inner self).
The relationship probable started out with Zee thinking she had to look after Karen since Karen is very awkward socially and meek. But I think Zee came to realize she liked having Karen around to talk too . Karen came to all of Zee's shows, Karen is Zee's lab partner, they work together on a play, they sit together a lot. Karen is one of the few people who can talk to Zee and calm her down. It just makes sense they would be pulled together.