The bigger they are, the harder they fall means that it is more difficult to beat stronger opponents, but we can beat them, and when they lose they suffer a bigger loss. Example: "Are you worried that he might be too strong?" Reply: "No, I'm not. He may be big, but the bigger they are, the harder they fall."

The word harder has two meanings here. First, it is harder (more difficult) to beat them; and second, when they lose they go down harder (more painfully). Example: "Those guys thought they would never lose. But we finally beat them. And look at them crying now." Reply: "The bigger they are, the harder they fall."

The bigger they are, the harder they fall means that bigger people are harder to knock down, but when they go down they hit the ground harder. You can say this to encourage a smaller competitor. Example: "Good luck, and remember: The bigger they are, the harder they fall."