Only 2 weighings are required.
Group the 9 boxes into 3 sets of three. Weigh one set against another. If a pan goes down, this means that the heavier box is among the set on that pan. Pick any two of those boxes and weigh them against each other. If one pan goes down, you have found the heavier box. If they balance, the heavier box must be the one you set aside. Now, if the sets balance at the beginning, you know that the heavier box is in the set you put aside. Weigh those boxes against each other to identify the heavier box.