[Old Thomas]

Is your house of modern construction? Our code, based on the IRC and our previous code back to 1984 required a minimum of 40 lbs. per square foot for the first floor and 30 for the second floor. That is uniform loading, point loading has to be determined based on many factors.
Bear in mind that if you overload your floor it will sag long before it fails. Generally residential floors are constructed such that a maximum load will cause the floor to deflect no more than 1 inch for 360 inches if span. It is referred to as L=1/360. That ratio makes a floor that does not appreciably bounce when you walk on it.
An exact answer depends on the construction, bracing, span, species of lumber, size of lumber, what supports it down to the earth, etc. An engineer earns his fee.
You mentioned 6 feet by 2 feet, 12 square feet. A quick answer is about 500 lbs in modern construction.