  We introduce the weighted greatest common divisor of a tuple of integers and
explore some of it basic properties. Furthermore, for a set of heights
$\mathfrak w=(q_0, \ldots , q_n)$, we use the concept of the weighted greatest
common divisor to define a height $\mathfrak{h} (\mathfrak p)$ on weighted
projective spaces $\mathbb{WP}_{\mathfrak w}^n (k)$. We prove some of the basic
properties of this weighted height, including an analogue of the Northcott's
theorem for heights on projective spaces.
