We introduce dynamically weighted tree transducers (dyn-wtts), a weighted generalization of top-down tree transducers with regular look-ahead in which rule weights are determined by external tree weighters mapping input trees to values in a commutative semiring. The general framework allows for any kind of device defining a weighted tree language to serve as a tree weighter. In this paper, we focus on weighters implemented by different classes of tree automata and show how the resulting classes of weighted tree transformations relate to one another and to known classes. In particular, we show how conventional top-down weighted tree transducers (with and without regular look-ahead) can be expressed as dyn-wtts, also in the linear and non-deleting cases.