Carbon Fiber? You're probably thinking of kevlar reinforced tires, which is a common puncture-proofing belt material thrown into the design of a tire's casing.

For 27 x 1.25, there's the Continental Ultra Gatorskin. They make a 32-630 size of them, and I'd trust those just fine. I've been riding the 700 x 28 version all year, and only wore out my first one at about 3200 miles; and I'm heavier than you by 40 pounds.