Aircraft have several 'significant' weights - basic empty weight, max takeoff weight, max taxi weight, max landing weight in specific configuration etc. Since you did not specify which weight you are looking for, I will write about max takeoff weight - which is the maximum weight (aircraft, fuel, payload combined) you are allowed to be at - at the beginning of takeoff roll.
B747 and B777 come in different versions - with variations in weights.
B747-100 - 734,000 lbs (oldest)
B747-100B - 750,000 lbs
B747-200 - 800,000 lbs (early models)
B-747-200 - 833,000 lbs (late models)
B747-400 - 875,000 lbs (up to, some are less)
B747-400ER - 910,000 lbs
B747-8 - 970,000 lbs (projected)
B777-200 - 545,000 lbs
B777-200ER - 656,000 lbs
B777-300 - 660,000 lbs
B777-200LR - 766,000 lbs
B777-300ER - 775,000 lbs
personal experience (B747)