It could be wear, there does seem to be a faded curve in the "J".
As for vector art, you need a dedicated program for that. I don't use one, so I can't recommend any.
A useful tool in Gimp that may help you with script (and other curved shapes) is the "Paths" tool.
Working large and then resizing is a good idea, but works better for images than for text. Just cleanup the blurring with a 1 pixel paintbrush or eraser.