  The entropic way of formulating Heisenberg's uncertainty principle not only
plays a fundamental role in applications of quantum information theory but also
is essential for manifesting genuine nonclassical features of quantum systems.
In this paper we investigate R\'{e}nyi entropic uncertainty relations (EURs) in
the scenario where measurements on individual copies of a quantum system are
selected with nonuniform probabilities. In contrast with EURs that characterize
an observer's overall lack of information about outcomes with respect to a
collection of measurements, we establish state-dependent lower bounds on the
weighted sum of entropies over multiple measurements. Conventional EURs thus
correspond to the special cases when all weights are equal, and in such cases,
we show our results are generally stronger than previous ones. Moreover, taking
the entropic steering criterion as an example, we numerically verify that our
EURs could be advantageous in practical quantum tasks by optimizing the weights
assigned to different measurements. Importantly, this optimization does not
require quantum resources and is efficiently computable on classical computers.
