In the absence of any qualifiers (the 2nd argument to Serial.print(), the value is converted to a string, and sent one character at a time.
Since the value you want to send is larger than what fits in a byte, you would need to store the value in an int, and then use highByte() and lowByte() to extract the two bytes. Then, you would use Serial.write() to send the two bytes.
If you send strings (the default behavior), you can send them using println(), so that a carriage return/line feed is appended, and have Processing look for that combination as the terminator.
What should I be listening to from processing
Whatever the Arduino is sending.