Extra damage on an attack favors more attacks. Since those with high BAB already get more attacks, I don't think you need to break up the damage bonus more with different progression.
By the same token, ways to get extra attacks like TWF would really dominate if it was a straight bonus, so I'd suggest something more like Str or Power attack in regards to weapons.
This does invalidate Weapon Specialization, and probably a few other things. Well, makes it nigh meaningless. The BAB 20 character with Weapon Spec only gets a small relative bonus over the straight BAB 20 character. Other bonuses to damage, like sneak attack, are also made slightly less important as a ratio of total damage done. And the few spells that increase BAB like Tenser's Transformation and Divine Power become a bit more powerful. Tenser's was a bit on the weak side, it might be okay. Just think of the ripples of this.
If you're using armor as DR, are you using defense bonus or something to offset the lowered ACs, or are people just hitting more? If it is the latter, maybe force a 1:1 power attack on everyone (even ranged). So a BAB 10 character has +5 to hit, +5 to damage (with a 1h weapon). This helps hitting so often and rewards high BAB with higher damage. It also brings the low BAB characters into hitting the low percentage of the time that they should. Make the power attack let the character specify, so they can do more damage or even chose less damage if they want accuracy. That would keep it some value.
Whatever you do, you may want to consider it precision damage like sneak attack and skirmish. Doesn't work again foes with no weak points (immune to crit), only applies on the first hit of manyshot and things like that, etc. That uses the rules to have the flavor that high BAB gives you the ability to know how to better place your blows, but against that plant creature there really isn't such a place.
Good luck,
=Blue(23)