Light-weight was coined as an opposite to heavy-weight PMBOK-like or Prince2-like methodologies which bring a lot of hassle to be implemented properly. You know, all these documents procedures etc. We don’t need them. We’re going to be light-weight. We’ll put people over processes. But wait, people should be organized in some way or they’ll be wandering around with no clear goal. We shall better have some techniques which will allow us to direct their efforts. We’ll have planning games, stand-ups and strict timeboxing. We’ll add some software development techniques as must-haves: test driven development and pair programming sound good. Wait, are we already surrounded by all these principles? Do we have as much formalism as we used to? Is that possible we are heavy-weight? Ouch.
I’m not trying to say agile is bad although some will read above paragraph that way. The thing I’m saying is that agile is pretty formal. And that’s perfectly understandable. Actually agile replaces some techniques we used in big old methodologies with some others which are more fun (user stories are more fun than 100-page Word document filled with requirements sent by a client) and in some situations are more useful and more productive. Which doesn’t mean they’re less formal.
Actually in the area of software development it was agile which brought much formalism. E.g. XP set up strict rules how code should be developed talking not only about code itself but also about developers and their interactions. From developer’s perspective old-school formal methodologies are probably way less formal than informal agile techniques.
Agile means formal, but formal doesn’t mean bad.