Starting in the 1990s mid, for software development, the team of process mavens began advocating a new model. This new process model was lightweight, as opposed to the heavy weight plan-driven models and espoused by groups like SEI (Software Engineering Institute) at Carnegie Mellon. It required fewer process controls and less documentation. Actually, it was the agile development process model in words. The agile development process model is also type of incremental model.
Agile was target at smaller teams of developers and small to medium-sized software projects. Furthermore, it was intend to allow developers teams, to adjust quickly, to changing customer demands and requirements. And much more quickly than the plan-driven models it proposed to release completed software. Agile development model works from the proposition that is working code of the goal of any software development project.
Then the development team should spend most of their time writing code, while not writing documents, because the focus is on working software. These processes give this name “the lightweight methodologies / agile methodologies”. See the Agile Manifesto for the agile development process model and its goals.