heavy armors should be more vulnerable to blunt weapons
Heavy (plate) armor is best suited for spreading a blunt impact over a larger area.
Classic "anti armor" weapons are effectively piercing weapons like a bec de corbin - or even a sturdy spear.
swords that are typically the best weapons should offer a good compromise but be expensive and less specialized
Swords had the best PR agents. The myth surrounding them is the best thing about them.
And while Zweihänders looked cool, they had very few specific roles. They were never a primary weapon.
Simple spears or maybe polearms are useful in a medieval battle. Maybe a short sword or dagger for close-in work but there won't realistically be any duels with long swords - or the space for using them in a formation.
You're exaggerating the "heavy" aspect of hammers. Those were not 20 kg hammer heads. =P
Typically they were one-handed and used for armor piercing because the wielder would not use the hammer head - that only provided the mass - but the spike on the other side.
I'm not sure if armour can be pressed into any convenient rock/paper/shotgun scheme.
Plate / chain: superior against slashing, very good against blunt because it's never worn without a gambeson (or equivalent)
No clear weakness. Weighted piercing weapons are still your most realistic hope of getting through it.
Leather armour can be just about anything else. Good ones offer some protection against slashing, too, because "battle edges" were not exactly razors. That would ruin the weapons far too quickly. Swords were mostly used for piercing because a straight thrust is hard to defend against and doesn't make you as vulnerable as a wide arching (hollywood) swing.
A weapon designed to pierce plate armour would be equally effective against leather armour. Plate armor does not slow/hinder a fighter as much as is "common knowledge". Leather would actually have to be much stiffer as a whole if it were to provide any protection and the better weight distribution of plate (vs chain) enabled knights to literally do somersaults.
(except for especially heavy tournament plate which would be rather dense thing to wear in a battle)
The "evasion property" of leather armour alone would not make it better against blunt weapons. It's cheaper. That's about it.
A system of damage avoidance vs damage mitigation for armour seems more useful.
Plate does not just make you slower. The always curved surfaces are designed to deflect blows - not just stop them cold. So "good" plate could actually increase the avoidance stat. Early plate wasn't as sophisticated or comfortable to wear so it was a lot "bulkier". But that's a matter for the research tree.
With damage avoidance and mitigation there would be sliders to adjust armour to "useful" values.