It is very difficult to increase the size of the wrists as there are no muscles there. Only bone and tendons. But you can try forearm exercises as in gym. It will get little better. Regarding your weight issue, it all depends on your height as well and so BMI. You will start gaining weight as you grow older so don't worry about that. But it's better to start some regular sport or gym. If you are active and fit, weight doesn't matter.