To add a bit more detail to snaggles post:
Both weapons are on independent timers. For simplicity, let's say you are holding two 20 delay weapons, and you have 100% haste. This means both weapons have 10 delay. 1 delay = 0.1 seconds, so both weapons are swinging every 1 second.
Dual wield has a skill check every time you swing your offhand weapon. If you fail the skill check, the offhand swing doesn't do damage. So if your current dual wield skill gives you a 50% chance to dual wield, then on average your offhand will swing every other second, because you fail 50% of your dual wield checks. When testing this stuff yourself via parsing, remember that double attack is a thing. If you have double attack trained, you wouldn't necessarily see exactly 2x mainhand swings for every offhand swing in this scenario, as both weapons are also triggering double attacks.
Melee characters get a main hand damage bonus, which maxes out at 11 for 1 handed weapons. The main hand damage bonus is a considerable portion of your damage, so the rule of thumb for your main hand weapon is generally to use your fastest weapon. Ratio does still play a factor, so this isn't an ironclad rule. For example, Wurmslayer (25 damage/40 delay) would still do more damage than a rusty dagger ( 3 damage/24 delay), even though the dagger's delay is significantly lower.
Offhand weapons do not get a damage bonus, so you generally just want to put your best ratio weapon in offhand to maximize damage. There are obviously exceptions to this rule as well. If you have two weapons with similar ratios, but one weapon has a damage proc, the proccing weapon may out dps the other weapon, even if the other weapon's ratio is slightly better. Some weapons like Ragebringer and Swiftwind provide ATK buffs, which improve the DPS of both weapons. So that is another scenario where the ATK buff may benefit you more than using a weapon with a slightly better ratio.
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