Power estimation of software processes provides critical indicators to drive scheduling or power capping heuristics. State-of-the-art solutions can perform coarse-grained power estimation in virtualized environments, typically treating virtual machines (VMs) as a black box. Yet, VM-based systems are nowadays commonly used to host multiple applications for cost savings and better use of energy by sharing common resources and assets. In this paper, we propose a fine-grained monitoring mid- dleware providing real-time and accurate power estimation of software processes running at any level of virtualization in a system. In particular, our solution automatically learns an application-agnostic power model, which can be used to estimate the power consumption of applications. Our middleware implementation, named BitWatts, builds on a distributed actor implementation to collect process usage and infer fine-grained power consumption without imposing any hardware investment (e.g., power meters). BitWatts instances use high-throughput communication channels to spread the power consumption across the VM levels and between machines. Our experiments, based on CPU- and memory-intensive benchmarks running on different hardware setups, demonstrate that BitWatts scales both in number of monitored processes and virtualization levels. This non-invasive monitoring solution therefore paves the way for scalable energy accounting that takes into account the dynamic nature of virtualized environments.