The big counterweights are NOT at the base of the tower. The tower does not experience a bending moment from the load but remains dynamically balanced atop the tower at all times.
Moveable counterweights are on the opposite side of the tower from the load and much heavier. Along with the cable winding equipment and motors, at their most inward positon they exactly couterbalance the unloaded boom with the hook fully retracted.
As the load moves outwards or increases in weight the counterweights move outwards to compensate, maintaining balance.