Well, here is the thing; I don't think so.
Now I may be looking at this in a different manner entirely. Despite what they are stat wise, you have to consider something else. Their rank, and thus, the material they are made out of,
Lance are slender, with a pointed tip, thus they might be lighter. Axes have a big blade and small handle, the material needed for that may be heavier. Sword can be balance, but can give and take depending on the sword.
Over all, at the very least, you should categorize the weapons by type, and then basically do a Heroes stat way. Where Axes will have more Weight, Lance being the lightest, and sword being a nice in between.
I had originally thought of this from a material standpoint rather then gameplay, so feel free to ignore my vote and answer.