There’s a whole scale of [“standards of proof”](https://en.wikipedia.org/wiki/Burden_of_proof_(law)#Standard_of_proof_in_the_United_States) ranging from “some evidence” to “beyond a reasonable doubt.” “A preponderance of evidence” is right at the halfway mark: the burden is met if the evidence is 51% likely.
Fwiw this is also the lay meaning of the phrase, as well. “Preponderance” is just “the quality or fact of being greater in number.”
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