The burden of proof is what is called preponderance of the evidence. It is not as high as criminal court which is "beyond a reasonable doubt". Preponderance of the evidence in lay terms essentially means that the court weighs both petitioner's and respondent's evidence and makes a determination based upon which one carries greater weight. Bear in mind that as the petitioner you have the initial burden to carry the greater weight. If you meet that burden, then respondent has to show and provide evidence that sufficiently rebuts your claims.
This is not intended as legal advice and does not create an attorney-client relationship.