First-principles density-functional theory is used to study the phase stability/instability and anomalies in the formation of the higherature bcc phases of XZn (X = Cu, Ag, and Au) alloys. Although from perhaps a naive point of view, their properties are expected to monotonically depend on the noble-metal (X) column position in the periodic table, this is not the case. For example, the middle-column AgZn alloy has a lower bcc order-disorder (critical) temperature than the CuZn and AuZn alloys above and below in the column. It is shown that this and other nonmonotonic behaviors can be explained in terms of a competition between atomic-size effects and X-atom d-orbital spatial extent. For example, charge-density studies and pair-potential modeling of XZn alloys show that the effective Ag-Zn bond is significantly weaker than either the Cu-Zn or Au-Zn bond at their respective equilibrium lattice constants. We find that an increased atomic-core size effect initially weakens the X-Zn bonding as one goes from CuZn to AgZn, but then the larger d-orbital spatial extent for higher principal quantum numbers becomes a more dominant effect and increases the bonding from AgZn to AuZn. This study is focused on the highly symmetric cubic higherature phases, where relative bond-strength magnitudes should be far more important than any bond-directionality effects; the lattice parameters, bulk moduli, elastic constants, Debye temperatures, heats of formation, and order-disorder temperatures for the bcc phases of the three XZn alloys are calculated and compared with experiment.