Is body fat genetic?

I am a female, five feet tall and about 127 lbs. I am not satisfied with my size. I am not obsessed with weight but with the way I look. I am very strong and have plenty of muscle. It just happens to be covered by a thick layer of fat. Yes, it runs in my family. On my father's side everyone has trouble with their weight.

I am writing to you because I don't understand why I am not losing weight. I am a vegan. I have no dairy products and no fat content in my diet. Except for the occasional pat of margarine and fried falafel, I don't see why I haven't lost weight because I just cut the dairy products out about two months ago. I have been a vegetarian for 9 years. I ride a stationary bike twice a week in my target heart rate zone. I work out with weights and do calisthenics in my room every night. What is wrong? Is there another factor I am not considering? Glands? Do I just need to be patient? I like being big, I just don't want it all to be fat.

Thank You.