This article contributes an architecture-centric methodology, called AABA (Architecture-centric Agile Big data Analytics), to address the technical, organizational, and rapid technology change challenges of both big data system development and agile delivery of big data analytics for Web-based Systems (WBS). As the first of its kind, AABA fills a methodological void by adopting an architecture-centric approach, advancing and integrating software architecture analysis and design, big data modeling and agile practices. This article describes how AABA was developed, evolved and validated simultaneously in 10 empirical WBS case studies through 3 CPR (Collaborative Practice Research) cycles. In addition, this article presents an 11th case study illustrating the processes, methods and techniques/tools in AABA for costeffectively achieving business goals and architecture agility in a large scale WBS. All 11 case studies showed that architecturecentric design, development, and operation is key to taming technical complexity and achieving agility necessary for successful WBS big data analytics development. Our contribution is novel and important. The use of reference architectures, a design concepts catalog and architectural spikes in AABA are advancements to architecture design methods. In addition, our architecture-centric approach to DevOps was critical for achieving strategic control over continuous big data value delivery for WBS.