Heavyweight architecture means you are running complicated infrastructure software like J2EE with complicated API's on a small cluster of expensive SMP machines.
Lightweight architecture means you are running straightforward, open source software stacks with service oriented API's on large clusters of commodity machines.
There are four common ways of achieving a lightweight architecture. Three of them are open source solutions, and the fourth is Microsoft's attempt:
LAMP - As many of you know LAMP is my favorite lightweight stack.
LAMP runs a vast majority of the massively scalable websites out there, and is also the favorite deployment stack for most of the "Web 2.0" crowd, including Friendster, Facebook, MySpace,…