If the shape is separated outlne or are two shapes it works as usual (weld the points and maintain the width of the static point (BTW I suggest the final width to be an average of the original points line width...))
In this example there are only one shape (outline only) but is valid for two shapes and for non variable line width.
I move the selected point with the move point tool (with or without autoweld checked, it doesn't matter do the same with space key press) to be welded to the point on the left.
This is the result. As suppoused no new line is created and the two points are welded
But if I do exactly the same with a continuous outline shape this is the result:
Before:
After:
I think this is a bug.
Regards
Genete