I'm assuming (due to lack of indentation) that you have print(to_weird_case(string)) outside of the function in order to call it. If so, the NameError you encouter is due to you calling to_weird_case() with the parameter string but this variable doesn't exist so you get an error.
You don't have to include this since the testcases call the function automatically.

Codewars comments support markdown and html so you are able to section your code which includes indentation using 3 backticks. Use this so that I don't have to manually indentate your code.

You want it escape route (for it to stop running) to be length of the current recursion equal to 1 since otherwise it will return an empty string("1"[1:] will return an empty string). Change it to len(str) == 1.

Sorry was going to reply to your comment later since I'm tired.