Thyroid cancer, like most cancers, is due to a complex interaction between the environment and your body. For that reason, either your genetic makeup or the world in which you live can contribute to your likelihood of developing thyroid cancer or any other type of cancer. If anyone in your family has a history if head and neck cancer, or if you have a history of exposure to radiation in the past, you are more likely to develop thyroid cancer at some point.
If you have low thyroid hormone levels, that could be for several reasons. Some of these reasons do, indeed, make you have a slightly higher rate of thyroid cancer. This higher rate could be, in part, due to the fact that people with thyroid hormone variations are more likely to be screened for thyroid cancer, but that is probably not all of the reason for the increased risk. For that reason, it is important to follow up with your doctor
at regular intervals.
Fortunately, thyroid cancer generally is very slowly progressive and responds very well to treatment, meaning that you have a window of opportunity to treat it should it arise. Please speak with your doctor about your concerns.