I feel the balance between the melee weapons is fine tbh (item tweaks aside, like barmaces, shields, lhbs etc). 1H+shield for best protection, 2h for best all round weapons, polearms for best spamming or shieldbreaking. All 3 are viable, they just require different tactics. My kill/death ratios are the same for all 3, 4-5 to 1 on duel, 2-3 to 1 on battle/siege.
1h without shield is certainly unbalanced though, if you look at it as a seperate class. 1h without shield is fine in a duel, but in any kind of group situation you'll lack the range of a 2h/polearm and the protection of a shield. I quite like madjackmcmad's suggestion of buffing 1hs without shields, but like eponi pointed out, that would be very hard to balance correctly.
My suggestion would be a more advanced inventory system. Something that takes into account the size and/or weight of a weapon to determine what you can carry. Maybe a slots system, where you have, for instance, a back slot, 2 belt slots and a body slots and then let the item size/weight determine which slot it can occupy. It would have to be worked out more thoroughly though.
