Runners often take around 1500-1700 steps per mile (thats ~40,000 steps during a marathon!). With each footstep, the amount of force pounding the ground can exceed 2.5 to 3 times your body weight. Because running involves having both feet off the ground during the swing phase of the gait cycle (which occurs after the lead foot pushes off), the impact involved in running is much higher than walking where you keep one foot in contact with the ground at all time. Thus, heavier runners tend to be more susceptible to impact-related injuries than lighter runners (knee and foot problems are common). But anyone who does more than their body can handle is at risk of getting injured regardless of their weight.
Kate, your youth and the walking you do now is a plus. Assuming you are in good health and have no relevant injuries, the 24 week Walk-to-Run program Trae mentioned looks to be a good way to get you started running. The Galloway run/walk approach to doing a marathon that Ed G mentioned is a popular one for those who dont have a strong running background. But lets not worry about how youll get to running 26 miles until we know how youre handling running 30 min/day regularly 6 months from now. Thats plenty to work on for now Good Luck!