If multiple states qualify for activation based on their properties, character studio uses the clip associated with the one with the higher precedence first. If more than one state has the same precedence, then the one with the greater weight is played first.
At the default value of 0, the animation will start once the state is active. If the value is 66, the animation will start playing two-thirds of the way in once the state becomes active. You can also randomize where the animation starts by specifying a Animation Start Deviation value other than 0.