In both Online and Ad-hoc modes, armor and weapons are automatically restricted (grayed out if not on INFERNO) by level through difficulty -- which disables use of high level weapons in an lower difficulty game and HP/armor will be normalized between players. Only on INFERNO are all weapons and full HP/armor allowed. However, if you achieve 70% completion (weapons and stages; shown on the main screen) for either Storm1 or Pale Wing, the weapon and HP/armor restriction for all difficulties will be selectable (thus be able to be removed/turned on). You can then host a room on any difficulty with all weapons available.
In short, to remove armor and weapon restrictions, achieve 70% Completion on either Storm1 or Pale Wing.