I'm going to go against the crowd and say I suspect your weight does play a factor in career opportunities based on a couple of observations:
1. Once you get to a certain level, you look upwards at people above you and realize that they all seem to be over-achievers not only in their career but in other parts of their lives as well. My direct superior at a large company I was recently with was a long distance runner and one of the pioneers of BMX riding in his native country. Another guy above me was a distance cyclist who took two weeks off from working to cycle the Alps with a group of other insanely fit people. A senior director played volleyball competitively. And so on.
Theory: A lot of getting "in" with a group of people is emotional - they have to feel like you naturally fit with them. If you don't seem to be the type who excels in all major facets of your lifestyle, they'll notice and your odds of getting in go down.
2. Would you naturally look to hire someone who looks or dresses slovenly to execute a job that requires precise, decisive action? Considering the state of BMI in the West I'd hope that you would, but I wouldn't be surprised if people immediately have a thought otherwise. If you're "lazy" about your health or appearance, maybe people think that translates into mental processes as well?
I've wondered all of this for a while myself and it's caused me to work on dropping the ~7 pounds of weight I should drop - I've biked roughly 1200 km this year to that effect. If you're in NYC, you're near some really great trails and should consider doing the same!