Predictive uncertainty--a model’s self-awareness regarding its accuracy on an input--is key for both building robust models via training interventions and for test-time applications such as selective classification. We propose a novel instance-conditional reweighting approach that captures predictive uncertainty using an auxiliary network, and unifies these train- and test-time applications. The auxiliary network is trained using a meta-objective in a bilevel optimization framework. A key contribution of our proposal is the meta-objective of minimizing dropout variance, an approximation of Bayesian predictive uncertainty, We show in controlled experiments that we effectively capture diverse specific notions of uncertainty through this meta-objective, while previous approaches only capture certain aspects. These results translate to significant gains in real-world settings–selective classification, label noise, domain adaptation, calibration–and across datasets–Imagenet, Cifar100, diabetic retinopathy, Camelyon, WILDs, Imagenet-C,-A,-R, Clothing-1.6M, etc. For Diabetic Retinopathy, we see upto 3.4\%/3.3\% accuracy & AUC gains over SOTA in selective classification. We also improve upon large-scale pretrained models such as PLEX.