  We formulate Vojta's conjecture for smooth weighted projective varieties,
weighted multiplier ideal sheaves, and weighted log pairs and prove that all
three versions of the conjecture are equivalent. In the process, we introduce
generalized weighted general common divisors and express them as heights of
weighted projective spaces blown-up relative to an exceptional divisor.
Furthermore, we prove that assuming Vojta's conjecture for weighted projective
varieties one can bound the $\log {\rm h_{wgcd}}$ for any subvariety of
codimension $\geq 2$ and a finite set of places $S$. An analogue result is
proved for weighted homogeneous polynomials with integer coefficients.
