  We investigate local and global weighted heights a-la Weil for weighted
projective spaces via Cartier and Weil divisors and extend the definition of
weighted heights on weighted projective spaces from arXiv:1902.06563 to
weighted varieties and closed subvarieties. We prove that any line bundle on a
weighted variety admits a locally bounded weighted $M$-metric. Using this fact,
we define local and global weighted heights for weighted varieties in weighted
projective spaces and their closed subschemes and show their fundamental
properties.
