Does juggling balls reduce the total weight of the juggler and balls?

Question

A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that since the man only ever holds one $3$-pound object at a time, the maximum combined weight at any given moment is only $195 + 3=198$ pounds, and the bridge would hold. I corrected him by explaining that the acts of throwing up and catching the ball temporarily make you 'heavier' (an additional force is exerted by the ball to me and by me onto the bridge due to the change in momentum when throwing up or catching the ball), but admitted that gentle tosses/catches (less acceleration) might offer a situation in which the force on the bridge never reaches the combined weight of the man and both balls. Can the bridge withstand the man and his balls?

Answer 1

the weight is greater than the mans weight since he has to apply force o the balls to juggle them up in the air

Answer 2

The man weighs the same, on average, whether he is juggling the balls or simply carrying them, for the same reason that an hourglass weighs the same whether it is running or not. When the sand grains are falling, they are weightless; but when a sand grain lands, it imparts additional force as it gives up the momentum it acquired while falling.