The densest possible layout of a 747 allows for 660 passengers. (Note that this is only possible in 747-300 and 747-400 models, so we will assume a slightly more common 747-400.)
The operating empty weight is 393,263 lbs. (This includes all flight personnel, the possessions of flight personnel, and all fluids necessary for operation, except for the fuel.)
The maximum takeoff weight is 875,000 lbs.
This allows for 481,737 lbs. of fuel, passengers, checked bags, and carry-ons. (See note below.)
The maximum fuel capacity is 57,285 gallons.
Aviation fuel weighs approximately 6 pounds per gallon.
This makes for 343,710 pounds of fuel.
This allows approximately 138,027 lbs of cargo, including passengers.
The average American citizen weighs 178 lbs.
At capacity, this would be 117,480 lbs. worth of passengers.
This leaves 20,547 lbs. for checked bags and carry-ons.
If each passenger checks one bag, and each bag weighs the exact maximum of 50 lbs, that would be 33,000 lbs worth of baggage.
Not including carry-ons, our theoretical plane is already 12,453 lbs. overweight.
NOTE: The 747-400, fully fueled with zero passengers, can carry 481,737 lbs. worth of cargo. The space shuttle Endeavor itself weighs only an approximate 170,000 lbs. The 747 could theoretically support the weight of 2.8 Endeavors.