NEW WEAPON QUALITY: Balanced
you take -1 to hit when simultaneously fighting with two weapons that are not both balanced weapons. In addition, some feats may not apply if noted in the feat description.
a balanced weapon costs 20 gp more to make than a regular weapon of the same kind. this cost is doubled for double weapons. masterwork weapons are automatically balanced weapons as well.
That is pretty much what masterworked weapons are anyway, so I don't see it as a necessary additional rule.
NEW RULES:
Two-Weapon Fighting:
any character who is proficient with all martial weapons can fight wielding a weapon in each hand.
when doing so, treat both weapons as one weapon; making one attack roll, and only applying bonuses to damage and extra bonuses (such as from a rogue's sneak attack, or the precise strike feat) once.
If either of the weapons does not have the balanced special quality, you take a -1 penalty to hit. you also take a -4 penalty for each of the following:
one of the weapons is not light
the weapon in your off hand is not light
the weapon in your off hand is exotic
I'm a little confused on the intent. And about one major part of your change in rules that aren't covered below.
Question 1: The goal is to make the penalties less (and not require the DEX to be so high) correct?
Question 2: How does "when doing so, treat both weapons as one weapon" factor into it? Mostly I mean, damage and benefit. Before fighting with two weapons gave you extra attacks "15/15/10/10/5" for example instead of "17/12/7". Now I'm not sure what this looks like. It is good you clarified the rogue and precision damage only applying once but it isn't clear if you get more attacks, more damage, higher critical (chance or modifier) or what exact benefit it confers.
NEW FEATS:
Two-Weapon Fighting
Prerequisites: Proficiency with all martial weapons, Base attack bonus +1
you avoid the -4 penalty for fighting with two weapons, one of which is not light.
I would change the prerequisite to
"Proficient with a martial weapon, Base attack +1"
from
"Proficiency with all martial weapons, Base attack bonus +1"
Unless there is a very good reason why they must be able to use ALL martial weapons. If you make that one change then it allows people from abnormal classes who trained up to be able to use the feats as well.
Ambidexterity
Prerequisites: Proficiency with all martial weapons, Base attack bonus +1, Two-Weapon Fighting
you avoid the -4 penalty for fighting with a one-handed weapon in your off hand.
I would probably roll this in with the base rules for Two-Weapon Fighting (including the feat). I have seen many professional duelists fight with two weapons - a primary foil and a parrying dagger - and the dagger goes in off hand not the sword.
Oversized Two-weapon Fighting
Prerequisites: Proficiency with all martial weapons, Base attack bonus +1, Two-Weapon Fighting
you avoid the -4 penalty for fighting with an exotic weapon in your off hand.
I would change the proficiency to
"Proficient with an exotic weapon, Base Attack +3, Two-Weapon Fighting"
instead of
"Proficiency with all martial weapons, Base attack bonus +1, Two-Weapon Fighting"
______
I don't think I need to repost the bit about magic weapons, which is by the way, to solve the problem that a +2 flaming burst, icy burst greatsword costs an extra 72,000 gold, but two +1, ____ burst shortswords only cost an extra 36,000.
The point being is that you have a higher chance of hitting with a +2 flaming burst, icy burst greatsword than with two +1 anything bust shortswords. Yes it costs less but you have less chance of doing the same damage or hitting as well. You do however get more attacks to hit with so there is that.