What operating system are you using? Also, do you have the latest version of the tablet software installed for your tablet? If not, I'd recommend downloading and installing that first to see if that helps.
It sounds like a pressure problem. Click 'Reset' in the tool settings panel when you have the pencil selected and see if that helps. If not, try increasing the pressure dial. If that still doesn't improve the situation, check the pressure settings in your tablet software.