Clearly you receive the bonus.

Honestly "equipped" it's outside Arkham jergon: no items are equipped even when used in the last combat. You use items, you devote hands to them, you exhaust items AND you have an equipment. But there is no definition of the word "equipped" in the rules that I'm aware of.

Sorry if my answer was misleading. I read your "equipped" as if you were intending "in play", it seemed to me the only logical reading. You have the item in play, you get the bonus to Fight checks.

For in-theme, I think it fits perfectly on all counts:

It's a tool first and foremost, as we've all said. Using it to smash gates/doors/coffins/chests for Fight Checks.

The bonuses in Combat should only be applied while equipping it because of what it is; the reduction to toughness is because a Sledgehammer is all about breaking through heavy and thick layers of stone/wood etc because it applies pin-point pressur in terrific force to a single spot. Thus, the Toughness reduction only when equiped.

I've always seen the +3 to combat as I have any other weapon's; it's the combat rating of how effective the given weapon is in general. The +1 to Fight is there because it IS a sledgehammer, which is in fact a powerful tool. Even in Call of Cthulhu, the actual pen-and-paper, as far as Melee weapons go, the sledgehammer is one of the most economical yet powerful weapons an Investigator can have. It's cheap, readily available at any hardware store and it actually has a damage rating of:

1d8 +2 +db (character's own damage bonus).

So yes. I think that this is likely exactly what it is; a very powerful, if not one of THE most powerful weapons in Arkham Horror because of it's utility and strength. The fact that cost is $6 may seem cheap but again, there is the luck factor of GETTING the sledgehammer in a shop on top of everything else and it is taking into account the theme of it.

Point is, I think the card was designed to be played as is; bonus upon bonus because that is how it's played in other games of the same setting (that is, Lovecraft).

The fact that cost is $6 may seem cheap but again, there is the luck factor of GETTING the sledgehammer in a shop on top of everything else and it is taking into account the theme of it.

That is not an adequate explanation, however. What that's saying is, "it's okay to price something poorly because it's rare." Well then, why isn't Healing Stone $3? The point of the pricing is to match the item's worth, and while the designers made some mistakes in the past (Press Pass, Old Journal, Elder Sign), the pricing is not arbitrary.

So, to reiterate, because the thing is $6, I believe that is adequate evidence that the Fight bonus is not applied to combat.