This common English saying, the bigger they are the harder they fall, derives from a truism, which is a true observation about the world, but is commonly used idiomatically. Let’s break it down!
Harder in this phrase means with greater force—and therefore, more painfully. It could be based on the idea of a tree falling; the taller the tree, the harder it will hit the ground when it falls, because it has a longer distance to fall and more weight (than a smaller tree).
We use this meaning of harder in other ways also. You can hit hard or press hard—with a lot of force. And when something hits you hard, that means it hurts.
But the idiom always concerns a person or organization, not a physical object. To fall here means to fail—to lose one’s money, social status, power, or happiness. Bigger means having more of these things. The “bigger” person who is falling might be a billionaire, a popular celebrity, a powerful politician, or an egotistical friend.
In other words, the more you have, the more you can lose, and the more it can hurt; whereas, a person who has nothing, has nothing to lose.
Since this phrase usually refers to a person who is “riding high” as we say (someone who has a lot), it is often spoken with a tone of satisfaction or justice. Or as an observation of the natural irony of life.
Nobody knows the true origin of this idiom, but many English speakers associate it with the story of David and Goliath from the Bible—in which the human boy David knocks down the giant Goliath by hitting the giant in the head with one stone, from a slingshot. The first recorded example of a similar sentence in literature is from the Roman poet Claudian in 303 BCE.