Some women w/cf stop having periods because of low BMI (body max index - weight relative to height) or weighing too little. As sakasuka said, it is the body's way of taking care of itself. If the body cannot nourish itself, then it cannot nourish a baby too. Low weight causes hormones to become unbalanced and without certain hormones, you cannot ovulate. If you don't ovulate, there is no egg to fertilize (which creates an embryo). Also, those hormones are needed to build the lining in the uterus that would nourish the baby through pregnancy, which is what you shed each month with your period.
When you are on birth control pills it provides hormones that your body may not be producing, which explains normal periods (or shedding of the lining) during that time.
Also, you said your period comes every 1 or 2 weeks. If it comes every 2 weeks and alternates bewteen heavy and light, you could be having mid-cylce spotting (the light periods) that some women get when they ovulate. The heavy would be a regular period (the shedding of the lining). If your cyles are short, that could still be ovulation spotting one and a half to two weeks after your last period. Everyone's cycles are different and each person's cycle can be a little off from month to month.
These are just some possibilties as to what might be happening. Your ob/gyn will be able to answer your questions more, just thought this might help in the mean time.