Weight matters more depending on what kind of riding you plan to do, and it generally matters more in things like wheels and tires more-so than the frame. Your bike(which was an awesome buy at $50, btw) is more of a beginner bike. Just ride it as is until you get some more experience and get a feel for what kind of riding you want to do. Carbon is also not at all a determining factor of a frame being worth upgrading. It all depends on what you want to get out of it. Carbon is the current big name bike company sales pitch. It is advantageous for some things, but it's not some sort of super material that's best for everything. For what it's worth, it's also more harmful to the environment than AL or steel. If you appreciate the nature you're riding around in then you might want to avoid the material that will s*** all over that nature in the long run.
