Let F=weight of a football player and C the weight of a cheerleader. 3F+2C=2F+6C. Subtract 2F from both sides: F+2C=6C. Now subtract 2C from each side: F=4C. So, assuming the footballers and cheerleaders have consistent weights (all the footballers are close to the same weight and all the cheerleaders are close to the same weight), 4 cheerleaders would be needed to match the weight of a footballer.
If you were doing this practically, when the two footballers from each side have left their respective sides, there should still be balance between the footballer and two cheerleaders on the left and the 6 cheerleaders on the right. If there isn't balance it would be necessary to take two different footballers from the left so that balance is preserved. Similarly, when two cheerleaders leave their respective sides it's possible that the combined weights of the cheerleaders on the left may not be equal to the combined weights of those on the right. But, it's only a mathematical problem, so no matter...