Modern software systems often provide a vast configuration space to enhance reusability and adaptability, but this configurability also significantly complicates bug finding. While existing static and dynamic variability-aware analysis approaches systematically explore the configuration space, they often suffer from scalability limitations. Conversely, grey-box fuzzing has demonstrated remarkable success in vulnerability detection through lightweight, iterative input space exploration, yet the state-of-the-art configuration fuzzers overlook the potential of integrating variability-aware analysis within the fuzzing process. In this paper, we present VAFuzz, a novel variability-aware fuzzer that integrates principled dynamic variability-aware analysis within the fuzzing process to enhance configuration space exploration. VAFuzz introduces new variability-aware seed selection and mutations to drive the fuzzing process. These are enabled by a new presence condition seed queue that tracks coverage and crash contributions across the configuration space, and a map that captures the relationship between data seeds and presence conditions. Our evaluation on a diverse set of programs show that VAFuzz outperforms the state-of-the-art configuration fuzzers on 21 out of 25 programs in terms of code coverage. It also detects more vulnerabilities than these baselines, including previous unknown bugs.