I am going to chime and say just do it. You're great for running I'm more into swimming (which I love) and getting into a pool in a swim suit stopped me from doing it for a while, but I just did it. I got the occasion curious look and then people stopped caring. I think it is was more about oh someone new walked in than anything else.
I say put on your headphones and go do what makes you happy. Remember you are whats important. I also think most people will be impressed and inspired that you're out there doing your thing.
Weird story...There is a show about kids at fat camp there is one girl who was 500 lbs and was down to 300 something when the show ended. At one point she did crunches as part of her exercise program. I have been kind of avoiding doing them because I thought I was too fat, whats the point, Im too heavy....and so on.
After I saw her I got my behind down on the floor and did my ab work.
My point here is you never know what people will think and it probably is way more positive than you think. I was reading something that said family and friends are harder on us than stranger, but someone else mentioned no we are probably the hardest on ourselves more than anyone else.
Anyway all this to say, GO HAVE FUN DOING WHAT MAKE YOU HAPPY