So I see the basis for interesting rules out of this.
For a DM, it's probably easiest to describe 1 attack roll as 1 swing.
There's a few things that get muddled, namely, the timing (6 seconds may be too long for some things, but as PCs get higher levels, it evens out).
I'd suggest that lighter weapons would be able to attack more often, and that heavier weapons attack less often. I could argue that with 3 weapons classes (Light, Medium, and Heavy) that Light gives 2 extra attacks (-5, -10), and Medium gives 1 extra attack (-5). You might get some interesting effects out of this, and it might level out the playing field for damage with light weapons versus heavy weapons.
For example: 1st level Bob needs a 9 to-hit (He's got +1 to-hit, versus a 10 AC enemy).
With a dagger (3 attacks, +1, -4, -9) he'd need 9, 14, 19 (% chance = 55%, 30%, 5%)
Based on that, his total averag damage (2.5 times %) would be 1.375 + .75 + .125 = 2.25
Wheras, with a Greatsword, he's just got 6.5 * 55% = 3.575
How's that interesting? Well, giving the smaller weapon guys will give them a slight increase in average damage, bringing them more in line with reality. In theory, they should do less damage, but attack more often, and have a comparable chance of hitting.
(side note, one could argue that if your bonus attacks are negative, nat 20's don't auto-hit, and therefore negate the bonus attack, which would basically put you back in the camp of you get 1 roll, but you swung your sword a whole bunch of times before that).
To further model reality, in theory, having a big weapon would make you harder to hit, when attacked by a smaller weapon. Namely, dagger versus longsword, bigger weapon should win (not just for damage, but the sword guy has an easier time hitting, and avoiding being hit by using his sword to block).
Additionally, there's a slew of other effects attack rolls can model (go see the Book of Iron Might) that can simulate shifting an opponent's position, or sword out of the way.
So the real question of all this is, does it add any extra fun? Does it make things more complicated? Adding an AC bonus per the weapon you are using isn't too hard. Rolling extra attacks might slow up the game, or become ridiculous at high levels.
Janx