I'm sorry to hear you're having trouble keeping the fonts consistent. When you're talking about changing the header or body text are you referring to the button in the below picture:
Or when you highlight the text and try to change it manually is it not changing to what you want? It's possible there is some excess html that might be hiding in the blocks that is preventing font from being changed.
I recommend reaching out to us at social_support(at)constantcontact(dot)com with your username, a reference to this post, and the e-mail campaign you are working on. We can take a look and see if something is interfering with your font.