Damage bonus adds a set amount of damage to each swing, it is only applied to mainhand weapons.
Because of this a faster, worse ratio weapon could outdamage a slower better ratio one.
For instance, let's take a 60 war in Kunark with a jade mace and a wurmslayer, which would they want to use?
Damage bonus at 60 is 11, so every mainhand hit gets 11 extra damage applied. Jade mace has a ratio of .5, while the Wurmslayer has a ratio of .625, clearly superior. However because the extra 11 damage is applied over twice as often in the case of the jade mace it will win in terms of dps output. How do we know that? We can use a simple formula which gives the "sweet spot" of weapon damage and divide by delay. The sweet spot is 2x weapon damage + damage bonus, This is usually the most common hit (other than min or max depending on mobs your fighting) and hits tend to be normally distributed from there).
For jade mace this gets us 9 x 2 + 11 / 18 = 29 damage per hit / 1.8 hits per second. Cancel the hits out to get a rudimentary form of damage per second (misses, duel wield, double attack, atk vs. mobs defense will all play into the actual formula). Reducing that gives you 1.611. Doing the same for Wurmslayer gives us 25 x 2 + 11 = 61/40 = 1.525. A good bit less damage than the jade mace.
This is why the general rule is keep your low delay weapon mainhand for the damage bonus and keep your best ratio weapons offhand sort of works. However, neither duel wield nor double attack fire 100% of the time, so offhand is going to naturally swing less. Because of this, if the offhand weapon ratio is superior enough to the mainhand, you'll lose dps by keeping it in your offhand.
Offhand also checks (or did on live) entirely independent of primary hand.
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