Weight and mass are two different things, would be my answer.

It the way the weapon is constructed is my guess, if you take the form of a big 2 handed war-hammer and remove the weight, you will (first off make the warhammer useless), second off you would still lose a lot of the momentum in the attack by wielding it in 1 hand, the core idea is, the weapon is made for you to swing it with 2 arms and apply as much force as possible (and as much of the war-hammers weight).

Sincerely
~ Kongdej

I am sorry, the enchantment only starts working when you touch the hammer with both hands... its a safety feature.

~ Kongdej

Well if we're talking magic, it could well have no weight but still the proper amount of inertia - meaning it still takes two hands worth of force to swing the thing, and it still hits like a two handed maul, it just doesn't take any extra effort to lift it. Imagine the magic as a constant upward force that cancels out gravity, it wouldn't propel the thing any faster when you swing it, you'd still need two hands.

Edit: it's a silly example, but this can occur in real life. As a thought experiment, picture a war hammer suspended from a blimp, hanging in midair at just the right height. It takes no effort to lift it, but to move the thing it takes enough force to move both hammer and the full weight of the blimp with it (blimps do have weight, just a little less weight (well.. density to be precise) than the surrounding air). Replace the upward force the blimp provides with 'magic', and voila, you have a 'weightless' hammer that takes a great deal of strength to actually swing.