Hey Jessica, I'm a bit behind on Orchid (500 left to go, YIKES!) so
you may have already had an acceptable answer. But thought I'd
offer my 2cents worth.
I've done this before several ways depending on the project.
1) Cut the line with a small blade then use a larger blade to
thicken the line. Though its difficult to cut with a large blade on
thin gauge initially, it works quite well to start with a thin blade
then simply make a line thicker. You may need to mess with the
angle that you hold the saw frame at to get this to work.
2) Use a thin disc-like bur to follow the line and widen it. This
only works if its a fairly straight line and the bur is the
thickness you desire. Also Dremel discs work well, but the line
would have to be dead straight. Both require a very steady hand.
3) Cut some 280 (appx) sand paper into thin strips and run it in the
grooves. I've also doubled up a thin strip by folding it in half
then putting it loosely in my saw frame like a blade, then running
it in the grove. This helps it to stay straight and not round the
edges of your line as much. This method and #1 are the ones i use
If you need a better description of any of this just drop me a note.