Bagnell Dam is what is known as a gravity type dam, meaning it is designed to impound water by shear size and weight. Others, such as the Hoover dam, utilize load bearing shapes, typically curved, to reduce overall mass.
Bagnell Dam was built using 553,000 cubic yards of concrete, and although there is no fixed number for converting concrete volume into mass (due to the different types of concrete) a rough rule of thumb is 1cu.yd concrete = 2 tons of weight.
As officially stated, we also have totals for the remaining structure:
Reinforcing steel (rebar) at 2,000 tons
Structural steel at 1,500 tons
Gates, trash racks and guides at 2,100 tons
Machinery for hydroelectric operations at 1,500 tons
For a grand total of 1,113,100 tons, or about 2.23 billion pounds! Now that is a chunk of concrete. By comparison though, Hoover Dam weighs 6.6 million tons, or about 13.2 billion pounds, despite its mass reducing curved design which distributes the majority of the lateral load to the canyon walls.
Update: April 2017 - Work should begin soon on additional post tension anchors and 66 million pounds (about 33,000 cubic yards) of concrete. That's a lot of concrete by any measure but only represents about 3% of the current weight. It's hard to imagine that relatively small additional weight would make a significant difference. The addition of 68 post tension anchors would seem to provide a greater impact insuring the dam never moves.