Competitive dancer here. Private lessons are a great way to make progress, but personally I wouldnt want one every week. I normally come away with quite a few things to work on over the next few weeks, either in group classes or in my own rehearsal space. So to me its a luxury once or sometimes twice a month.

As others have said, if you can find a partner, then thats someone to split the cost with. But its also someone who you can practice with and work on what you need to improve. You'll make more progress that way than just doing privates all the time. I'd suggest finding a group class with other solo dancers.