To bear out something means to confirm or provide evidence for something.
Example sentence:
When you are studying any matter, or considering any philosophy, ask yourself only what are the facts and what is the truth that the facts bear out. Never let yourself be diverted either by what you wish to believe, or by what you think would have beneficent social effects if it were believed. But look only, and solely, at what are the facts. (Bertrand Russell, 1959)