What you're asking for is not possible in PDF.
To elaborate, each path that is drawn in PDF has its parameters set by the current graphic state. This implies that each path drawn has a specific line-width (the whole path).
To deal with corners and end-points, you can use the line cap and join parameters (together with miter limit if you draw complicated shapes) but you correctly saw that these are only applied to the current path; not to connections between different paths. How you deal with such compositions between lines of different line width, is up to you.
Math is your friend...