You are looking at the wrong things when comparing outputs. While ultimate power is important, it's not the most important, especially on a machine designed for the road rather than the race track. Torque is what's king on the road. Power is just a measure of torque x RPM. More RPM gives more power for the same torque.
Most sports bikes, designed with a heavy track focus, are designed to produce maximum engine output high up the rev range. Ideal when you're riding flat out from curve to curve on a track with the rev needle bouncing around the red range and the engine screaming. Your average 4 cylinder sports 1000 produces around 75 - 80 lbft of torque at something like 10500 to 11500 rpm.
The ZZR1400/ZX14R produces just over 100 lbft of torque at 7500 to 8500 rpm. What's more, it produces much more torque further down the rev. range than a 1000 engine enabling stronger acceleration for longer without the need to change gear. Because of the higher torque output ultimate top end power, while roughly the same as the sports 1000, happens at a lower rpm. This, in turn means you can run higher gearing, this giving a more "relaxed" ride, to get the same rate of acceleration and same ultimate top speed (aerodynamics aside - which become way more important than power!!!).
One of the down sides of a 1400 though is that there are much bigger bits of metal "flying around" inside the engine, and these need to be controlled and managed, This, in turn, makes for heavier "chunky" components and more inertia.
As a result ultimate maximum rpm is reduced to avoid the engine throwing bits of itself away! Hence the matched top end power because a slower engine speed with more torque matches a faster engine speed with less torque. So, you can get the same result by either "screaming" a 1000 or being more relaxed on a 1400. For the road, especially on longer runs, the second option is often the preferred choice.
Enter the supercharger. This allows a 1000cc 4 cylinder engine to produce almost 90 lbft of torque at around 8600 rpm. For road use, that's a better than a "half way house" between the screaming 1000cc sports bikes and the relaxed 1400. Smaller engine components means less inertia but low down and mid-range torque to match a much larger engine. And, all of this is with a "neutered" engine. Get a reflash and the torque increases to around 100 lbft. That matches the 1400 engine!!
So, as a road rider you now get all the advantages of a 1400cc engine without a lot of the disadvantages. A very attractive option!! ;)
Now, to the bikes weight. The weight is NOT the supercharger. While I don't know what it actually weighs (help anyone???) it's a relatively small/light component. The problem is that, engine torque can be used to move the bike forward rapidly, or can be used to bend the bike in half!!! As the second option is not what we want, the frame and cycle components need to be up to the job of resisting being bent in half. More torque means "beefier" components. Thicker frame tubes, stronger swing arm etc. all come with a weight cost. Additionally, most sports 1000s are designed to handle a single person with the possibility of an occasional pillion on some. The H2 SX is designed to run with a pillion ... and luggage. That's another 80 to 130kg that the frame needs to manage while handling the sorts of forces associated with 150mph road speeds. Again, all of this adds weight. Compare the H2 SX to other sports tourers designed for 2 up plus luggage runs rather than rider only sports bikes and suddenly the weight doesn't seem so bad.
So, a long explanation. I hope it helps.