In short, you're probably no where near the level of weight required to break a rib, considering the information below. You're probably laying on a large padded area, you're more muscular than average (considering your avatar), and your bone density is probably quite a bit higher than average from weight training.
Your troubles could be related to having trouble breathing from the pressure on your chest.
According to biomedical engineer Cindy Bir:
"A quick, sharp blow that delivers some [740 pounds] of force has a 25 percent chance of cracking an average person's rib."
"'That doesn't means that below those values you won't have a fracture or above them you will,'" Bir said. The amount of damage a blow inflicts also varies due to factors such as the amount of muscle or fat covering a bone and the angle at which the blow lands, ...the age and health of a person, which can affect bone strength," the rate at which force is applied and the surface area to which its applied.
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