I've always attributed the name "Weapon X" to Logan during the time when he was a government-sanctioned assassin. In the Ultimates universe 'Weapon X" is the name of the program itself. The program designed to weaponize mutants for government purposes.
It's not as straight-laced and sterile as it sounds. At the core of Weapon X is the belief that mutants are not human and should not be treated as human. As we shall soon see, the conditions mutants are subjected to in Weapon X are brutal in the extreme.
The issue opens with a potential escapee.
The German mutant gives the Weapon X people a solid run but in the end he is caught and we get a sampling of the brutality I talked about.
And yes, it is Colonel Wraith. Wolverine's tormentor from the second issue whom Jean Grey chose to save. Thanks again Jean (you bleeding heart idiot).
Speaking of Wolverine, he is on the hunt for the Weapon X base. Apparently the operation is semi-mobile, uprooting itself and transfering locations every few months.
In his continuing effort to better Human-Mutant relations the Professor sends some of the X-Men on a speaking tour of Japan.
Japanese culture being the way it is, the X-Men are mildly shocked to find fascination instead of paranoia.