Choosing your weapon type

Dagger lowest

Scythe highest

Damage is the easiest way to tell your weapon choice

Axe highest one hand

Sword right under

Dagger lowest

Two handers

Gaxe polearm then scythe great sword somewhere in there

The damage does not reflect the weight

That algorithm is complicated to write out

It's more like what swings better with your str and dex

Haste and dual wield help with to but do not change your weight on the weapons on the effort involved to swing them