  We continue the study of thick triangulated subcategories, started in
arXiv:2007.02134, and consider thick subcategories in the derived category of a
weighted projective curve and corresponding abelian thick subcategories. Our
main result is that any thick subcategory on a weighted projective curve either
is equivalent to the derived category of nilpotent representations of some
quiver (we call such categories quiver-like) or is the orthogonal to an
exceptional collection of torsion sheaves (we call such subcategories big). We
provide several equivalent descriptions of big subcategories and explain that
they can be explicitly classified. We give some results clarifying the
structure of thick subcategories: in particular, for weighted projective lines
we prove that any admissible subcategory is generated by an exceptional
collection and any exceptional collection is a part of a full one. Apart from
the above, we study general properties of quiver-like categories. In
particular, we extend and simplify results from arXiv:2007.02134 providing
sufficient criteria for a triangulated or abelian category to be quiver-like.
