I'm a little taller and (just recently) a little lighter than you are, and I think you'll be fine. I'm about 230 pounds, down from 270 a year ago, and I rarely have problems with any of my bikes.
As you ride, try to anticipate big bumps and learn to cushion the shock by standing up and absorbing it with your arms and legs--don't just sit down and let it hammer you, which is hard on you AND the bike. Deflate the tires sl ightly on very rough roads and trails to increase control if you like, but it's really a matter of technique. A lot of us who started mountain biking before there was suspension really enjoy going out on a rigid bike (I still have my original Bridgestone from 1984, and ride it fairly often), so don't let anybody tell you you can't go anywhere you want.