Beyond a reasonable doubt.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
The government must prove every element of the offense beyond a reasonable doubt. In response to the second portion of your inquiry... It does not matter if it is a help or burden to the court. It is constitutionally mandated that a defendant shall not be convicted unless the government can meet this burden. Because the penalties associated with a criminal conviction are severe... There is no doubt that this is the best system in the world.