  Despite enormous efforts devoted to the study of the many-body localization
(MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin
chain in a strong random magnetic field is lacking consensus. Here, we take a
step back by exploring the weak interaction limit starting from the Anderson
localized (AL) insulator. Through shift-invert diagonalization, we find that
below a certain disorder threshold $h^*$, weak interactions necessarily lead to
ergodic instability, whereas at strong disorder the AL insulator directly turns
into MBL. This agrees with a simple interpretation of the avalanche theory for
restoration of ergodicity. We further map the phase diagram for the generic XXZ
model in the disorder $h$ -- interaction $\Delta$ plane. Taking advantage of
the total magnetization conservation, our results unveil the remarkable
behavior of the spin-spin correlation functions: in the regime indicated as MBL
by standard observables, their exponential decay undergoes a unique inversion
of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a
key quantity for capturing ergodic instabilities, as it increases with system
size near the thermal phase, in sharp contrast to its transverse counterpart
$\xi_x$.
