One way you could to this so that you have two different service types in use depending on the weight would be to add in a second USPS server behavior and set it to use the Priority Mail.
Once the second server behavior is on the page you can create an if statements around them so that if the weight if less than 13oz then use the first server behavior, and if it is over 13oz then use the other one. You could simplify this further by putting the if statement directly into the server behavior around the service type. That way is a little more advanced though and would require you to hand edit the code for the server behavior.
If you can add the second server behavior to the page I can show you how you would craft the if statement to use one or the other.