  Motivated by experiments on Pr2Ir2O7, we consider metallic pyrochlore systems
A2B2O7, where the A-sites are occupied by rare-earth local moments and the
B-sites host 5d transition metal ions with itinerant strongly spin-orbit
coupled electrons. Assuming non-Kramers doublets on the A-site, we derive the
RKKY interaction between them mediated by the B-site itinerant electrons and
find extended non-Heisenberg interactions. Analyzing a simplified model of the
RKKY interaction, we uncover a local moment phase with coexisting spiral
Ising-like magnetic dipolar and XY-like quadrupolar ordering. This state breaks
time-reversal and lattice symmetries, and reconstructs the B-site electronic
band structure, producing a Weyl Metallic phase with an intrinsic anomalous
Hall effect and an undetectably small magnetization. We discuss implications of
our results for Pr2Ir2O7.
