  A \emph{$\nu$-reliable spanner} of a metric space $(X,d)$, is a (dominating)
graph $H$, such that for any possible failure set $B\subseteq X$, there is a
set $B^+$ just slightly larger $|B^+|\le(1+\nu)\cdot|B|$, and all distances
between pairs in $X\setminus B^+$ are (approximately) preserved in $H\setminus
B$. Recently, there have been several works on sparse reliable spanners in
various settings, but so far, the weight of such spanners has not been analyzed
at all. In this work, we initiate the study of \emph{light} reliable spanners,
whose weight is proportional to that of the Minimum Spanning Tree (MST) of $X$.
  We first observe that unlike sparsity, the lightness of any deterministic
reliable spanner is huge, even for the metric of the simple path graph.
Therefore, randomness must be used: an \emph{oblivious} reliable spanner is a
distribution over spanners, and the bound on $|B^+|$ holds in expectation.
  We devise an oblivious $\nu$-reliable $(2+\frac{2}{k-1})$-spanner for any
$k$-HST, whose lightness is $\approx \nu^{-2}$. We demonstrate a matching
$\Omega(\nu^{-2})$ lower bound on the lightness (for any finite stretch). We
also note that any stretch below 2 must incur linear lightness.
  For general metrics, doubling metrics, and metrics arising from minor-free
graphs, we construct {\em light} tree covers, in which every tree is a $k$-HST
of low weight. Combining these covers with our results for $k$-HSTs, we obtain
oblivious reliable light spanners for these metric spaces, with nearly optimal
parameters. In particular, for doubling metrics we get an oblivious
$\nu$-reliable $(1+\varepsilon)$-spanner with lightness $\varepsilon^{-O({\rm
ddim})}\cdot\tilde{O}(\nu^{-2}\cdot\log n)$, which is best possible (up to
lower order terms).
