In legal claims before the court there are 3 distinct burdens of proof on the plaintiff.
We all know that in criminal cases the burden is "beyond a reasonable doubt". In some classes of cases, it is a lesser burden of "clear and convincing evidence". Personal injury actions carry the lowest burden, "greater weight of the evidence".
The greater weight burden is often described as "more likely than not". In practice it requires the weight of plaintiff's evidence to slightly sway the scales of justice in the plaintiff's favor. This is often a difficult concept for jurors who are accustomed to watching TV shows or movies portraying a criminal trial.