I'm very overweight and I
I'm very overweight and I started barefoot running a year ago. I had gained a modicum of fitness through working out with kung fu, and I had previous experience running, and I had been trying to build up to running for a couple years prior to my taking off my shoes. In fact, the year before I started barefoot running, I was using Jeff Galloway's run/walk method to train for a half marathon, thinking that the run/walk would be better for an overweight person getting back into running because of the rest periods. I ended up with a case of plantar fasciitis (which it's coming to light may have been due to a misaligned fibular bone, but I didn't know that at the time -- I thought it was my running shoes, and maybe they were partially responsible, but that it is all material for another post.)
I was worried about running barefoot while overweight, especially stress fractures. I was very methodical, using suggestions from Jason Robillard's book and Michaels Sandler about how to condition for barefoot running. I was extra-conservative and adapted their plans to an even slower approach. I think I went even twice as slow as they recommmended.
I consider that I had a lot of success, and got to the point where I ran a few 5Ks last year completely barefoot.
Not only that, as I've been researching the matter, I've concluded that running barefoot might even be a preferable way for an overweight person to start, because there are studies out there that indicate being barefoot reduces stress on joints, etc...
Checking with a doctor can be a good step, but I think they are mostly good to rule out heart conditions and that it doesn't matter too much whether you tell them you will be barefoot or not. (My husband went to medical school and I don't recall his having any lectures on barefoot running at all. Right now I think I know more about it than he does.)
I think it's important to consider one's experience with fitness in the past and one's state of fitness at present. It doesn't hurt to pre-strengthen muscles you'll be using for running by walking first. In fact, it is probably a good idea.
One last thing: Because of how slow I had to go in the beginning, it was not effective for me for weight loss because I couldn't get my mileage nor my speed up enough for that effect to kick in. In the long run, adding running to your life of any kind, shod or barefoot, can be helpful for weight management, but with the slow conditioning of barefoot running you might have to wait for those fruits.