The only reason why you'd have him drag the overweighted hammer around rather than casually carrying it around is that you want to convince the player that it's huge, massive and that it's gonna shake the ground as soon as they use it.
You can go for "superhero" that can carry that massive hammer like a golf club or for a regular hero with something special that let his do deathly blows with the hammer but doesn't change other aspects of his daily life (the hammer is still damn heavy when he's not "invested by a mighty god of revenge" or when he's not turning on the Anti-gravity system of the hammer).
Imho, that doesn't mean that you need to decide why he can do so unless you can come with a gameplay element (e.g. he needs to keep an eye on the power level of that anti-gravity system or the hammer will be useless) that is interesting and might worth a word of explanation. An alternative would be "fine, you've got the hammer, but it is too heavy for you to jump, so you'll have to leave it there, jump, toggle that switch, come back and pick it up" ... and if someone attacks you while you've left it behind ... too bad.