My personal opinion comes in two points. First, even if the weapon is the most important piece of gear in determining overall damage (which, as HardRock and Mapes have said, may not be the case), I don't really have much of a problem with that. In terms of fantasy lore, weapons tend to have the most focus in terms of a character's prowess as a warrior (which in game terms usually translates into DPS). Aragorn wields Anduril, the re-forged version of the legendary sword Narsil; Link wields the Master Sword; King Arthur wields Excalibur; Cloud Strife wields the Buster Sword; and there are many more examples like these. Tons of heroes (and villains) are known for their legendary enchanted weapons; much fewer are the characters known primarily for enchanted shields or magical armors. From a gameplay perspective, this may not be the best choice, but I personally think that it makes sense that the weapon determines a good portion of a character's power. If damage is going to be %-based (which I agree is a welcome change) then I feel that on a conceptual level at least, it doesn't feel wrong to have a lot of damage come from the weapon.
Second, I think that the best fix for this 'problem' is to greatly diversify the way that weapons work. Currently, the only differences in weapons is the base attack speed, and sometimes the weapon type (in case you have skills/passives that care about that sort of thing). Some special classes of weapons can roll special mods, such as +AP/APoC on wands, but by and large, weapons tend to all feel the same. I think that a lot of the 'problem' could be circumvented if weapons felt very different in how they acted. Now, how Blizzard could do that I'm not so sure. Probably my best guess at how to diversify weapons would be to associate an element with certain classes of weapons, and have elemental damage/'elemental damage skills deal X% more damage' affixes have a higher chance of rolling on specific weapons, or have those specific weapons have the possibility for a higher roll than otherwise possible.
To explain this system, you would break down weapons into each element: physical, fire, cold, lightning, arcane, poison and holy. As an exemplary possible breakdown, blunt weapons (hammers and maces), mighty weapons and fist weapons would be associated with physical, slashing weapons (swords and axes) would be fire, stabbing weapons (daggers) would be cold, shooting weapons (bows and xbows) would be lightning, casting weapons (wands and staves) would be arcane, ceremonial knives would be poison, and daibos and flails would be holy. These weapons would have a higher chance of spawning with elemental damage of their type, and a higher roll in their particular elemental damage affix than other weapons could roll. Thus, if you were playing a Barbarian, you might want either a hammer/mace or mighty weapon for a physical skill build, or an axe for a fire skill build. A Wizard might want a wand specifically for an Arcane-heavy build, or a dagger for a cold build, or even a bow (forgoing a focus) for a lightning build. This is not to say that this system would make it impossible for a non-aligned elemental affix to roll, just less likely. This would provide incentives for playing certain roles with certain weapons (or the reverse; wanting a certain weapon class because you're playing a certain build).
Another possible solution (taking a bit of a bite out of Dark Souls style) would be to classify skills by the kind of damage they deal. For example, for Barbarian skills, Bash would be defined as a 'blunt damage' skill, Cleave would be a 'slashing damage' skill, Ancient Spear would be a 'piercing damage' skill, Earthquake would be a 'casting damage' skill, and Weapon Throw would be a 'ranged damage' skill (for this purpose, synonymous with the previous definition of the 'shooting weapon' class). These definitions of skill damage types would correspond to weapon supertypes: hammers, maces, flails and fist weapons for blunt damage, swords, axes and mighty weapons for slashing damage, daggers and bows for piercing weapons (bows overlap piercing and ranged), bows and xbows for ranged damage, and finally wands, staves, ceremonial knives and daibos for casting damage. These weapon types would all carry an innate, passive bonus to skill damage with skills that share a damage type with them; there would be no penalty for skills that do not. Thus, the game does not force you to decide on a weapon based on your build, but it does give you a little bonus for picking a weapon class that complements your build. I think that a system like this could also help to fix some of the issues with weapons right now.
Ultimately, both ideas I presented are of course very early, first-thought ideas, and would have to be refined quite a bit to be worthy of inclusion into the game. That said, while I think that there are problems with both ideas, I also think that both ideas are capable of being refined into useful additions that help to solve the 'problem' that weapons pose in D3.
