  We study regularity in the context of ring spectra and spectral stacks.
Parallel to that, we construct a weight structure on the category of compact
quasi-coherent sheaves on spectral quotient stacks of the form
$X=[\operatorname{Spec} R/G]$ defined over a field, where $R$ is a connective
${\mathcal{E}_{\infty}}$-$k$-algebra and $G$ is a linearly reductive group
acting on $R$. Under reasonable assumptions we show that regularity of $X$ is
equivalent to regularity of $R$. We also show that if $R$ is bounded, such a
stack is discrete. This result can be interpreted in terms of weight structures
and suggests a general phenomenon: for a symmetric monoidal stable
$\infty$-category with a compatible bounded weight structure, the existence of
an adjacent t-structure satisfying a strong boundedness condition should imply
discreteness of the weight-heart.
  We also prove a gluing result for weight structures and adjacent
t-structures, in the setting of a semi-orthogonal decomposition of stable
$\infty$-categories.
