I think I have a weak immune system because I catch colds easily. Do I have a higher risk for cancer?

No. Unless you really have an impaired immune system such as hiv, cvid, hypogamaglobulinemia, catching colds dose not translate to an increased risk of cancer.
Not necessarily. Your immune system is probably quite normal. Many people are susceptible to colds without having immune deficiency. It is not likely that you are at increased risk for cancer. You should practice the usual preventive measures, i.e., do not use tobacco, maintain healthy weight, and do not drink or keep it to fewer than a drink a day.