It seems like you're really focused on your T's feelings about you and about the relationship between you.

Yes exactly! I think that part of me is like "What does it mean that she offered me two sessions a week? Does that mean she likes me?" or something along those lines. And I know that ideally I would like to talk about our relationship and my feelings towards her, but that would be SO hard for me b/c I like her so much and look up to her.
And I do think that weekly sessions would be beneficial for me in terms of me talking more. Farmergirl is right, that I need to look at it from a practical, financial perspective first, but I hate doing that because I know that then I shouldn't do bi-weekly sessions. I guess I feel frustrated because it's like, "Why would she offer me something that I want so badly but can't have?" Like it's better for me not knowing that she offers bi-weekly sessions, rather than knowing that it is available but not being able to go.