Deriving from first principles:
Battle Might : Barbarians add their Might mod to
their damage when using their barbarian melee
weapons (see chapter II for more details)
Possessions : Barbarians start with a dagger, their
melee Weapon of Choice, a missile weapon (bow +
12 arrows OR 3 javelins OR sling + 12 stones) and
a shield. Starting wealth is 3D6 x 5 silver pieces.
The incredibly phallic barbarian holding a sword two-handed does not seem supported by the text on page 10.
Melee weapons fall into four categories : Swords,
Spears, Daggers and Barbarian Weapons (see
next page for more details). In addition, these rules
will often refer to “battle weapons”, a term which
encompasses all melee weapons except daggers.
These weapons include big swords, huge battle
axes and even heavy maces or crude cudgels.
As their name implies, are normally only used by
Barbarians. Other warriors who try to use them
need a Might of 13+ to wield them properly and will
not gain the special damage bonus of Barbarians;
characters with a Might below 13 can only use
barbarian weapons using both hands (which
prevents them from using a shield).
These weapons have an Encumbrance value of 2.
Again, supporting the sword and board of barbarians.
Some characters are so strong they may be able to
wield the enormous weapons used by some Large
creatures (much like Herakles with his big club in
the illustration below). Such weapons have an
Encumbrance value of 4 and can only be wielded by
characters with a Might of 19 or 20, using both
hands. They roll 2D6 for damage but cannot benefit
from any special damage bonus. In addition,
characters who do use such weapons in combat will
strike at half their normal Initiative (rounded down).
Thus, we have a "you don't get to add your might mod when using stupidly large weapons."
Furthermore there are no references to "both hands" or "two hands" outside P.22 in both the primary and the supplemental books. Therefore, barbarians derive no in-game benefit from wielding their preferred weapons two-handed except those granted by the maze master. If the player desires it, modifying the "no bonuses" rule of truly large weapons to be an "Except for barbarians who can wield the weapons with both hands and.." if the maze master wishes to encourage that imagery.