Predicting viral evolution remains a major challenge with profound implications for public health. Viral evolutionary pathways are determined by the fitness landscape, which maps viral genotype to fitness. However, a quantitative description of the landscape and the evolutionary forces on it remain elusive. Here, we apply a biophysical fitness model based on capsid folding stability and antibody binding affinity to predict the evolutionary pathway of norovirus escaping a neutralizing antibody. The model is validated by experimental evolution in bulk culture and in a drop-based microfluidics device, the Evolution Chip, which propagates millions of independent viral sub-populations. We demonstrate that along the axis of binding affinity, selection for escape variants and drift due to random mutations have the same direction. However, along folding stability, selection and drift are opposing forces whose balance is tuned by viral population size. Our results demonstrate that predictable epistatic tradeoffs shape viral evolution.