Hi Talon,
Let them promote someone who isn't as qualified as you are. It's their loss when that person can't do the job. I certainly don't think you should pick up any of the slack. It may be your weight, but I think it is because they know what you can and can't do in the office, they just want to see how long you will put up with it. I have just started looking for a job, today was my first time out. I knew where I was going(5min down the road) it took me forty minutes to talk myself into going. I am 191 lbs. and I let my weight hold me back. I was proud after I left from applying. With every application and interview you fill out or attend, your confidence will build. keep up the good work on the weight loss, you've come a long way!!!