I'm surprised no-one has mentioned using a Touring bike with a triple chainset. They are definitely set up for climbing gradients, and if built around a high quality frame, may be slightly lighter than either a MTB or Hybrid.
On the subject of weight though, don't go too much on manufacturers figures - when a lot of the time those weights are quoted for small frame sizes with no mudguards or even pedals fitted. The weight that counts is the weight of a bike in real world running condition, fitted with all essential parts and any required accessories.
Bikes set up for practical use with mudguards, pump, and some basic first aid repair tools don't tend to end up much less than the high 20's pounds weight no matter what.