Upgrading everybodies magicks.

I have started crosstraining everybody in magic (As LP and gil allows), purchasing every spell I come across, and then buying the licensces as required. Is there any reason NOT to equip every party member with all magicks available?

Mostly it's the same problem with weapons except Balthiar's guns, and Fran's Bows. (I just gave Vaan a Javalin. Better attack value. May switch back to sword/shield as money allows. Also.. first thing I did is get the second best sword for Vaan and handmedown a mithril sword to Penelo (after a LP purchase).)

Why do characters need different weapons.

They don't need different weapons. Unless, of course the enemy has armor. This is when you'd want guns.

Of course, I'd focus on augments before magicks (with the exception of white and haste).

I would recommend you have everyone learn the white magic especially Cure, Cura, etc.
For weapon, it would be best to have at least one melee and one long range.
Because sometimes enemies attack can't reach the one with long-ranged weapon.