And the strongly recommended party setup for weak mode is...

White Mage/Shikari (Fran), Knight/Machinist (Balthier), Black Mage/Monk (Ashe), Red Mage/Shikari (Vaan), Machinist/Foebreaker (Basch), Black Mage/Time Battlemage (Penelo)

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White Mage/Shikari (Fran) is a high hp healer that is capable of using the 50 evasion weapon (Main Gauche) and a shield such as the 50 magick evasion shield (Aegis Shield). She also has the capability of using absorb shields like the Demon Shield for the Zodiark fight. White Mage/Shikari is a healer that takes hits better than most of the damage dealers.

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Knight/Machinist (Balthier) is the main damage dealer throughout most of the game. Very early in the game Balthier as a first job Knight will use Karkata which is almost a 100 damage one-hand sword with Confuse on hit. Mind you Confuse works on regular mobs and a large number of storyline bosses early in the game (Karkata can be stolen in Trial Mode stage 3). His second job Machinist is the highest damage dealer job available in weak mode. This is due to guns not having a strength calculation which is based primarily on your characters level. After Karkata, he will use Mithuna (the best gun in Final Fantasy 12: The Zodiac Age) which is purchasable through the bazaar near the middle of the game.

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Black Mage/Monk (Ashe) is a high damage caster with a lot of hp, Curaja, and Arise. There are a number of fights where magical damage is necessary which is why it's important to have a Black Mage even on weak mode. Monk as Ashe's second job has the benefit of giving her a much larger amount of hp. 

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Red Mage/Shikari (Vaan) is an all purpose buffer of Bubble and Protect with so-so heals and the ability to equip guns (unlocked with the esper Shemhazai) which are the highest damage weapons in weak mode. Red Mage can also use guns with Dark Shot and Dark Robes (with access to mystic armor from Red Mage) for the dark elemental boost if you would like to attempt Yiazmat (the hardest fight in the game outside of trial mode). They can optionally use Oil while using Wyrmfire Shot on tough regular mobs but, very few late game bosses are not immune to oil. He will also have access to Ardor, Blizzaga, Thundaga, and Darkga and will be able to use most White Magic, Black Magic, Green Magic, and Arcane Magic.

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Machinist/Foebreaker (Basch) is a high hp job combination like Knight/Machinist. It helps to have a different second job for your Machinist so that some of the licenses aren't shared in weak mode. Breaks have an extremely low chance of landing in weak mode but, have a large effect on never ending hp mobs like Hell Wyrm and Yiazmat. Even if you aren't going to attempt Hell Wyrm and Yiazmat, Foebreaker is an excellent second job combination for a damage dealer Machinist when playing on weak mode.

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Black Mage/Time Battlemage (Penelo) is used because having two Black Mages helps out significantly in weak mode. Black Mage/Monk is a good alternative option for Penelo because she will have a much higher hp than Black Mage/Time Battlemage. Time Battlemage as a second job is used for the added utility and because it is important to have different job combinations on weak mode to avoid shared licenses that can't be used by two characters. Time Battlemages has to be paired with a mystic armor class on weak mode or they will not have enough mp which is why Black Mage is the perfect pair for a Time Battlemage. As a Time Battlemage, Penelo will have the advantages of being able to use the Berserk spell on tough caster mobs like White Mousse and Mindflayers and she will have Hastega near the end of the game without putting Famfrit on a Machinist. Famfrit can then be given to the Black Mage/Monk for Arise.