Preferred Arms

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Swords

Knight (42%)
Squire (38%)
Geomancer (25%)
Thief (25%)
Chemist* (~1%)

Knives

Thief (50%)
Wizard (33%)
Chemist (25%)
Ninja (25%)
Dancer* (~2%)

Axes

Geomancer (50%)
Knight (20%)
Squire (19%)

Flails

Blue Mage (33%)
Priest (33%)
Ninja (25%)
Squire (19%)

Spears

Lancer (75%)
Samurai (25%)

Knight Swords

Knight (38%)

Katanas

Samurai (75%)
Geomancer (25%)

Ninja Blades

Ninja (50%)
Thief (25%)

Bows

Archer (40%)
Bard (25%)

Crossbows

Archer (40%)
Squire (25%)

Staves

Priest (67%)
Time Mage (60%)
Summoner (20%)

Rods

Wizards (67%)
Summoner (60%)
Calculator (20%, Blue Mage 17%)

Books

Calculator (50%, Blue Mage 33%)
Mediator (40%)
Oracle (25%)
Summoner (20%)

Poles

Oracle (75%)
Time Mage (40%)
Lancer (25%)
Calculator (20%, Blue Mage 17%)

Guns

Mediator (60%)
Chemist (25%)
Archer (20%)

Harps

Bard (75%)

Fabric

Dancer (75%)

Bags

Chemist (50%)
Dancer (25%)
All Classes* (~1%)

Unarmed

Mimes (100%)
Monks* (98%)

(The Bag chance* is omitted from this list… additionally, a weapon category that is forced via PreferredArms is marked with ~.)

Squire

Swords (40%)
Crossbows (25%)
Axes (18%)
Flails (18%)

Chemist

Bags~ (50%)
Guns (25%)
Knives (25%)
Swords* (~1%)

Knight

Knight Swords~ (38%)
Swords (42%)
Axes (20%)

Archer

Bows~ (40%)
Crossbows~ (40%)
Guns (20%)

Monk

Unarmed~ (98%)

Priest

Staves~ (67%)
Flails (33%)

Wizard

Rods~ (67%)
Knives (33%)

Time Mage

Staves~ (60%)
Poles (40%)

Summoner

Rods~ (60%)
Staves (25%)
Books (15%)

Thief

Knives~ (50%)
Ninja Blade (25%)
Swords (25%)

Mediator

Guns~ (60%)
Books (40%)

Oracle

Poles~ (75%)
Books (25%)

Geomancer

Axes~ (50%)
Swords (25%)
Katanas (25%)

Lancer

Spears~ (75%)
Poles (25%)

Samurai

Katanas~ (75%)
Spears (25%)

Ninjas

Ninja Blades~ (50%)
Flails (25%)
Knives (25%)

Calculator

Books~ (50%)
Rods (25%)
Poles (25%)

Blue Mage

Flails~ (35%)
Books (30%)
Rods (18%)
Poles (18%)

Bard

Harps~ (75%)
Bows (25%)

Dancer

Fabric~ (75%)
Bags (25%)
Knives* (~2%)

Mime

Unarmed (100%)

Certain classes have preferences in the Equip Item abilities. I'll list the 'default' list, then the preference lists, including the classes under this designation. If the class doesn't appear under the preference designation, it uses the normal list.

Equip Knife (normal)

Ninja Blades (36%)
Knives (36%)
Rods (29%)

Equip Knife (Priest, Time Mage, Oracle, Thief, Ninja, Dancer)

Rods (43%)
Ninja Blades (29%)
Knives (29%)

Equip Knife (Mediator)

Knives (43%)
Ninja Blades (29%)
Rods (29%)

Equip Knife (Chemist)

Ninja Blades (36%)
Rods (36%)
Knives (29%)

Equip Knife (Calculator, Samurai, Wizard)

Ninja Blades (43%)
Rods (29%)
Knives (29%)

Equip Knife w/ PreferredArms***

Knives Pref: Summoner, Mediator
Ninja Blades Pref: Knight, Wizard, Samurai, Calculator
Rods Pref: Chemist, Priest, Time Mage, Thief, Oracle, Ninja, Dancer

Equip Sword (normal)

Swords (38%)
Katanas (36%)
Knight Swords (26%)

Equip Sword (Knight)

Katanas (43%)
Swords (32%)
Knight Swords (25%)

Equip Sword (Samurai)

Swords (37%)
Knight Swords (34%)
Katanas (29%)

Equip Sword (Geomancer)

Knight Swords (36%)
Swords (32%)
Katanas (32%)

Equip Sword (Thief)

Katanas (37%)
Knight Swords (34%)
Swords (29%)

Equip Sword (Squire)

Katanas (36%)
Knight Swords (35%)
Swords (29%)

Equip Sword (Ninja)

Katanas (38%)
Swords (38%)
Knight Swords (24%)

Equip Sword w/ PreferredArms***

Swords Pref: Archer, Calculator, Dancer
Katanas Pref: Knight, Thief, Ninja
Knight Swords Pref: Squire, Geomancer, Samurai

Equip Axe (normal)

Axes (36%)
Flails (36%)
Staves (29%)

Equip Axe (Wizard, Bard, Oracle, Squire, Calculator non-Blue)

Staves (43%)
Axes (29%)
Flails (29%)

Equip Axe (Knight)

Flails (43%)
Axes (29%)
Staves (29%)

Equip Axe (Geomancer)

Flails (36%)
Staves (36%)
Axes (29%)

Equip Axe (Priest)

Axes (43%)
Flails (29%)
Staves (29%)

Equip Axe (Ninja, Blue Mage)

Axes (36%)
Staves (36%)
Flails (29%)

Equip Axe w/ PreferredArms***

Axes Pref: Priest, Lancer, Ninja, Blue Mage
Flails Pref: Knight, Time Mage, Summoner, Geomancer
Staves Pref: Squire, Wizard, Oracle, Calculator (non-blue), Bard

Equip Gun (normal)

Guns (43%)
Books (43%)
Harps (14%)

Equip Gun (Thief non-forced)

Guns (57%)
Books (29%)
Harps (14%)

Equip Gun (Thief forced)

Guns (63%)
Books (25%)
Harps (13%)

Equip Gun (Monk, Ninja non-forced)

Books (57%)
Guns (29%)
Harps (14%)

Equip Gun (Ninjas forced)

Books (61%)
Guns (25%)
Harps (14%)

Equip Gun (Calculator, Oracle, Summoner)

Guns (43%)
Books (29%)
Harps (29%)

Equip Gun (Chemist)

Books (43%)
Guns (29%)
Harps (29%)

Equip Gun (Mediator)

Harps (43%)
Books (29%)
Guns (29%)

Equip Gun w/ PreferredArms***

Guns Pref: Summoner, Thief, Oracle
Books Pref: Chemist, Archer, Monk, Priest, Wizard, Time Mage, Bard
Harps Pref: Mediator, Calculator

Equip Bow (normal)

Bows (50%)
Crossbows (50%)
Bags (1%)

Equip Bow (Samurai, Squire)

Bows (64%)
Crossbows (38%)
Bags (1%)

Equip Bow (Mediator, Bard)

Crossbows (64%)
Bows (38%)
Bags (1%)

Equip Bow (Archer)

Bows (43%)
Crossbows (43%)
Bags (14%)

Equip Bow w/ PreferredArms***

Bows Pref: Squire, Knight, Samurai
Crossbows Pref: Chemist, Mediator, Bard
Bags Pref: Archer
NO Bag Pref (Bow or Crossbow): Monk

Equip Polearm (normal)

Spears (43%)
Poles (43%)
Fabrics (14%)

Equip Polearm (Knight, Archer, Thief)

Spears (57%)
Poles (29%)
Fabrics (14%)

Equip Polearm (Wizard, Summoner, Mediator, Dancer)

Poles (57%)
Spears (29%)
Fabrics (14%)

Equip Polearm (Calculator, Oracle, Time Mage)

Spears (43%)
Poles (29%)
Fabrics (29%)

Equip Polearm (Samurai)

Poles (43%)
Spears (29%)
Fabrics (29%)

Equip Polearm (Lancer)

Fabrics (43%)
Poles (29%)
Spears (29%)

Equip Polearm w/ PreferredArms***

Spears Pref: Knight, Archer, Time Mage, Thief, Oracle
Poles Pref: Wizard, Summoner, Mediator, Samurai, Dancer
Fabrics Pref: Lancer, Calculator

This is a bit complicated, but will add roughly a 50% chance for a unit to be unarmed. This chance increased to 100% if Martial Arts was forced.
Martial Arts has a very small chance to be forced on a character with Punch Art as a secondary. This is similar to Monster Skill and Throw Item appearing on units with Talk Skill and Item. When this occurs, the unit is never unarmed. (Although this doesn't guarantee that all units with both Punch Art and Martial Arts is unarmed… Martial Arts could've rolled as a support by coincidence.)

Excluding PreferredArms (-preferredarms) ONLY equalizes your chances of the classes default weapon

* There's also a universal bag chance for every class. This chance is slightly higher for female units. This chance varies from class to class, but in general this chance is around 1% (Monks have the highest chance at this, at 2.5%). This chance still exists for Chemists and Dancers, who get Bags innately, but this chance instead gives Swords (Chemist) and Knives (Dancer). Mimes are the only class that cannot equip Bags. Instead their 'Bag Chance' gives them access to another upgraded Armor type.

*** If PreferredArms is rolled, and the class randomly rolls into this Equip skill, this weapon category will be forced. Sometimes, this will differ slightly from normal percentage values. Also, some classes simply have no forced preference (if it isn't listed under any category), and will refer to the default chance list.