Most people will use illustrator when creating vector files and use the Pen or Pencil tool to draft out the outlines and shapes of their design.
Once finshed select the artwork and expand appearance. This will ensure the stroke weights appear as shown on screen.
Object > Expand Appearance
Alternatively it is possible to use Live Trace to create vectors from a black and white image.
Place the file onto the art-board and select:
Object > Live Trace > Create and Expand
You may find that the object will need some tweaking to get it exactly how you would like it.