I weigh 250, and I learned the hard way: Pump those tires up when using the silly little lightweights that they sell you with the bike. #1 - They puncture easily, no matter what you weigh, and, #2 - heavy riders pinch 'em alot more than you think.
I find that a breaking point is at 28mm. I can use Tissue Tires when they are that size, but not less. The ultimate solution for the big guys, especially if you are aggressive, are Armidillo 23mm. Yes, I know they're heavy, I know they're like rolling on a cold garden hose, but you won't be going home because of a pinch flat or a minor fleck of glass.
I run my Army's at 125 in back and sometimes 110 in front for a bit of cush and a little more steer traction.