It does sound like your spindle is a bit light for the yarn you are trying to spin. I was able to find a cool 'device' at the hardware store to add a bit of weight. In the picture, take a look at the 2nd spindle from the left. Under the whorl is a picture of the 'device'.
It slips on the spindle and has a rubber screw that you can tighten with an allen wrench. It keeps the spindle balanced and makes a spindle more versitile!