1. 4 balls on the left-hand side of the scale, 4 on the right, to determine which group of 4 has the heavier ball.
2. Of those 4 which we know has the heavier ball, divide 2/2 between right/left sides of the scale to find which has the heavier.
3. Repeat with 1/1 to find which is heaviest.

I'm hoping there's a more clever way where in step 2 you could put 1 on the left and 2 on the right to finagle the heavier ball out of 3 segments (1 left, 2 right, 1 not weighed), but I can't think of it.

I think 3 weightings at most, possibly 2.

1. 4 balls on the left-hand side of the scale, 4 on the right, to determine which group of 4 has the heavier ball.

2. Of those 4 which we know has the heavier ball, divide 2/2 between right/left sides of the scale to find which has the heavier.

3. Repeat with 1/1 to find which is heaviest.

I'm hoping there's a more clever way where in step 2 you could put 1 on the left and 2 on the right to finagle the heavier ball out of 3 segments (1 left, 2 right, 1 not weighed), but I can't think of it.