How to make my wife's bike lighter? Is it worth the cost?
Difficult to say without knowing more about the bike, but I'd trade it in for a better bike; Huffy has a rep for low-end, tank-like bikes. From your description, you'd need to replace the frame and front fork to see any significant weight savings. 

Something with an aluminum frame like a hybrid bike would probably be easier to carry up the stairs, even though aluminum will give you a harsher ride. 

Suspension forks are heavy, particularly on low-end bikes. Suspension usually makes sense for off-road riding. If your wife mostly rides on pavement, you can get a bike without suspension of any kind.