The increased file size was "due to the increased amount of content" at launch, including map files for Warzone, as well as the Zombies mode, and the fact that a lot of content from Modern Warfare II carries over to Modern Warfare III.

If all you want to do is play the multiplayer version and you're happy to forgo the full visual experience excluding "high-rez" assets, then the absolute bare minimum install is 79GB. Add the single-player campaign sans high-rez assets and you're looking at 149GB.