The sand in the falling column does not contribute to the weight reading. But you can easily show from Newton's Second Law in the form F = dp/dt that the extra impact force of the falling sand exactly equals the missing weight of the total falling column of sand. Thus, while the sand is falling and impacting, the weight of the hourglass is equal to its weight when no sand is falling.
But initially, as the sand starts falling, there is "missing weight" in the column before the sand hits bottom, so the hourglass grows momentarily lighter. Similarly, at the end there a few moments while the impact force remains constant as the falling column decreases to zero, so the hourglass grows momentarily heavier. The movements of the laser spot on the blackboard faithfully trace out the graph of the weight of the hourglass as a function of time.
