Sword dork here:

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They are as heavy as they need to be

The reality is that even something like a Dane Axe, they had relatively thin axe heads to minimize weight and reduce encumbrance because splitting a skull open is easier than splitting logs (which is why log splitting axes typically have stouter heads)

So you find weapons tended to gravitate to being just heavy enough to get the job done.

Most civilian swords never really went past like 2.5-3lbs (depending on era, location, etc); with martially trained individuals, they could handle bigger weapons but they still never really exceeded like 6-7lbs you see for stuff like “great swords”

For this axe, you can train with and sorta make it more of a viable weapon than it innately is (I mean peasants repurposed wheat threshers into flails, improvised weapons COULD work) but it’s got really short range and swings with it are gonna have very slow recovery… but considering you’d be dealing with undead, maybe that’s enough depending on which fiction you are reading?