I'll tell you, I came from a lot worse shape than you did. Granted i've got a muscular figure, I was still WAY out of shape. I started BJJ @ 5'9 and 290. 6 months later i'm down to a pretty lean 210. I've got 30 more lbs before my goal weight for BJJ, but all it takes is time and practice and dedication. Change your nutrition as well if you already haven't, you'll feel your energy increase dramatically.
Also something really opened pandoras box for me, was controlling my breathing. Once I did that (and it took me about 2 months to figure it out) things got a TON easier. I was able to roll for a lot longer and play with a lot more things.
Go in with no ego onto the mat, and learn everytime you either get dominated or tapped. Ask whomever you're rolling with how they got there, whats a good defense. If you're rolling with a white belt and it happens, ask an instructor to take a look, you will both learn from it.
Also after playing a top game, as a big guy at first, you might find that (im guessing you have strong legs from carrying the weight, because I certainly do) the guard is something that you can also be very strong at. About 2 months before the PanAms when I was doing hard training, it just opened my eyes to the guard game that I could play.
So just stick with it, discover yourself in BJJ. The rewards are priceless.