How does shielding compete with nuclear charge with respect to atomic mass, and the Periodic Table?

Going down a Group, a column on the Periodic Table, the valence electrons are still the same. As we descend the column, while the nuclear charge $Z$ increases, the electron count increases proportionally. The increased electron count shields the increased nuclear charge, and ionization energies become correspondingly lower. The valence electrons are also further removed from the nuclear core, and their attraction to the nucleus should also decrease.