  We examine the results of Chiral Effective Field Theory ($\chi$EFT) for the
scalar- and spin-dipole polarisabilities of the proton and neutron, both for
the physical pion mass and as a function of $m_\pi$. This provides chiral
extrapolations for lattice-QCD polarisability computations. We include both the
leading and sub-leading effects of the nucleon's pion cloud, as well as the
leading ones of the $\Delta(1232)$ resonance and its pion cloud. The analytic
results are complete at N$^2$LO in the $\delta$-counting for pion masses close
to the physical value, and at leading order for pion masses similar to the
Delta-nucleon mass splitting. In order to quantify the truncation error of our
predictions and fits as $68$\% degree-of-belief intervals, we use a Bayesian
procedure recently adapted to EFT expansions. At the physical point, our
predictions for the spin polarisabilities are, within respective errors, in
good agreement with alternative extractions using experiments and
dispersion-relation theory. At larger pion masses we find that the chiral
expansion of all polarisabilities becomes intrinsically unreliable as $m_\pi$
approaches about $300\;$MeV---as has already been seen in other observables.
$\chi$EFT also predicts a substantial isospin splitting above the physical
point for both the electric and magnetic scalar polarisabilities; and we
speculate on the impact this has on the stability of nucleons. Our results
agree very well with emerging lattice computations in the realm where $\chi$EFT
converges. Curiously, for the central values of some of our predictions, this
agreement persists to much higher pion masses. We speculate on whether this
might be more than a fortuitous coincidence.
