Skewed balances

You are given weights 1,2,3,4,5,6,9. Discard one of them, and hang the rest on the scale below, so that it balances as drawn on one of the pictures below. Then switch two of the weights around, so that the scale balances as shown on the other picture. Judging by the reaction of my local guinea pigs puzzle group, this is a bit trickier than it looks.