Large-scale testing is crucial in pandemic containment, but resources are often prohibitively constrained. We study the optimal application of pooled testing for populations that are heterogeneous with respect to an individual's infection probability and utility that materializes if included in a negative test. We show that the welfare gain from overlapping testing over non-overlapping testing is bounded. Moreover, non-overlapping allocations, which are both conceptually and logistically simpler to implement, are empirically near-optimal, and we design a heuristic mechanism for finding these near-optimal test allocations. In numerical experiments, we highlight the efficacy and viability of our heuristic in practice. We also implement and provide experimental evidence on the benefits of utility-weighted pooled testing in a real-world setting. Our pilot study at a higher education research institute in Mexico finds no evidence that performance and mental health outcomes of participants in our testing regime are worse than under the first-best counterfactual of full access for individuals without testing.