Can rapid weightloss cause a light period?

Yes: Yes you can have a change in your menstrual cycle with significant weight loss and with increased exercise.

Yes: The main reason for light periods is change in hormone levels. Causes for what seems to be a light period can include: thyroid problems, eating disorders, excessive exercise, initial periods for a girl, use of an intrauterine device, oral contraceptives, perimenopause & implantation bleeding in early pregnancy which rarely occurs.