Have a knowledgable person look at the tires close up while you're on the bike. When you're on the seat, you can see them bulge out a bit, but it's hard to tell how low they actually are.
I weigh about 270, but am riding an old mountain bike, 26x 1.75 or 2 or whatever they sell at Walmart (they show like 6 different sizes on the box). Anyway, I run about 45-50 psi and that's fine. I can see some sideways bulge in the tire, but there's plenty of spring left, too.