Weight is a factor, but shouldn't be a problem for you as you are not that overweight. Injuries occur when you 1) Don't warmup correctly 2) Running technique is bad, 3) bad shoes and 4) trying to do too much. Start with a 2,5km run and see what happens. Find a nice rhythm and monitor your kness, calves and hips for any signs of pain. If there is nothing, then slowly increase the distance. When you reach your desired distance, increase the speed.
To give you an idea. I weigh 92kg (my BMI looks bad, but it is due to muscle) and run 10km every 3rd day. The only reason I don't run everyday is due to swimming and cycling taking up the other days.