First of all, publishing once a week is a great way to hold yourself accountable if you are struggling with consistency so I say go for it regardless of the income.
Finances depend on where you are publishing. If you plan to publish on Medium the best way to kick start your income would be to submit your work to bigger publications. If you are planning on building your own brand the income will be much slower because that kind of thing takes a long time to build.
When I first started writing on Medium, publishing once a week, I believe I earned about a fiver a month, at that point, I was not submitting to any publications.
Income depends on a few things, a pre-existing audience, social media from other sites can pull over a few readers so you may do better if you have a large following. That being said it’s better to get started early and build up your presence even if your social media following is small.
My advice would be to focus on building consistency because ultimately that habit is what is going to make or break you as a writer.
Sorry, I couldn’t be more specific, but the nature of the way that Medium pays(by reading time) means that it’s impossible to predict how much you could make. Hope this has given you some clarity ❤