Three weighings suffice. There are two different techniques for solving the problem. Let the balls be numbered 1 thru 6.
Weigh (1,2) vs (4,5), then (2,3) vs (5,6), then (3,1) vs (6,4).
All weighings involve one ball on each side of the beam balance. First weigh 1 against 2. If these are equal, then weigh 1 against 3, otherwise weigh 3 against 4. The reader may work out what the third weighing should be.