I'm new ish to running and started off not far short of 19st. I'm now under 17 and dropping, and have done two half marathons.
I started running after a disparaging comment about my weight from someone I didn't know from Adam. I used him as the motivation to train harder. I wanted to see his face at the end of the race so I could stick two fingers up at him.
Worked for me. I used to care what people thought about me running but not now. They can all sod off. I acknowledge everyone I meet, walkers, runners, dog walkers, the lot. Nearly always get a nod or hello. It's an ego boost I like