Answer
The spinning gyroscope will precess more rapidly.
Work Step by Step
See equation 10.33, which gives the precession angular speed: $\Omega = \frac{wr}{I\omega}$. If weight is added to the free end, that has the same effect as increasing $w$. This increases the precession angular speed $\Omega$. It takes less time to precess 1.0 revolution than it did before.
