I couldn't figure this out until I put an 'oh' in front of it - 'oh you are, are you?'
It can show that the speaker is surprised by the information they just heard, and probably would have some kind of criticism about it if they were to continue talking. It can have a tone of sarcasm or irony. In your example:
'We are partners' (if talking about business partners)
'Oh you are, are you?' ( '... that's funny because you're both lazy and never finish anything you start, so good luck with your business - you'll need it.')
'We are partners' (romantic partners)
'Oh you are, are you?' ('... that's strange because I just saw you on a date with a different person last night.')
The most I've heard a phrase like this used is between a parent and child, or between romantic partners. It shows (humorously, in my opinion) that the person who says it, disagrees with what you say you are going to do, and will probably follow the phrase with something else you need to do, or a reason why you're not allowed to do what you intend. It also has the tone of needing to ask permission to do something, not just saying you are going to do something.
"Mom I'm going over to John's to play."
"Oh you are, are you?" ('.. think again, you still haven't done your homework/you're still grounded and you can't go anywhere/it's too late to go outside and play.')
**If there's another context for 'you are, are you' I couldn't think of it. If my explanation doesn't fit with your original text, then I would have to see the original to figure it out.
(not a teacher, just a language lover)
Student or Learner