High-overhead; baroque; code-intensive; featureful, but costly. Especially used of communication protocols, language designs, and any sort of implementation in which maximum generality and/or ease of implementation has been pushed at the expense of mundane considerations such as speed, memory use and startup time. Emacs is a heavyweight editor; X is an *extremely* heavyweight window system. This term isn't pejorative, but one hacker's heavyweight is another's elephantine and a third's monstrosity.
Opposite: "lightweight". Usage: now borders on technical especially in the compound "heavyweight process".