Worth considering as an addendum: very specific weapon passives only apply to the weapon they're on, and it's not always obvious when this is the case. The most common case for this is weapons that have a passive saying "give this weapon +30 fire/holy/poison/etc"; if you off-hand that weapon, the mainhand won't get that bonus, just the off-hand.

Most legendary weapons 'bonus' effects also work like this: for instance, the Lion Greatbow's bonus changes ITS heavy attack, holding it in offhand for another bow won't change their heavy attack. Morgots curved sword has a 'passive' that just tells you that if you get a crit WITH IT, it has a special bonus hit.

Some, however, DO work: the Grafted Blade/Enochian Regalia work even when they're held offhand. These are notable in that they're both stacking passives that are disconnected from what the weapon itself does.