If you decide to go out Friday and at the end of the meal she decides not to offer to pay you could say something along the lines of "Now I don't want you to be embarassed but if you're not in a position to help with paying for meals / drinks, then I completely understand and we can take turns cooking at eachother's homes" or something like that. The ball is in her court then.
Also, being tight is a trait that many people have - we all have a friend that decides they're ready to head home when it gets to their round, or the friend that orders a pint of Stella on their round but only has a half of fosters on their own! It would be sad to end a relationship on a crappy trait that many people have - I think you should raise the issue this week or it will eat at you and you will end up resenting her, and if she is a gold digger then you are better off knowing now and get it done and dusted asap!
Good luck, and let us know how it goes x