Counting Drinfeld modules with prescribed local conditions

We give asymptotics for the number of Drinfeld ${\mathbb{F}}_q[T]$-modules over ${\mathbb{F}}_q(T)$ of a given height, which satisfy prescribed sets of local conditions. This is done by relating our problem to a problem about counting points on weighted projective spaces. Our results for counting points of bounded height on weighted projective spaces over global function fields may be of independent interest.