Their computer doesn't actually "measure watts," but makes an estimate based on speed and known setup procedures - so as an absolute value, you may be off. However, if you set up the KK the same way each time, I've heard from folks that the KK is consistent in its measurements when comparing to previous rides, and at the end of the day that's probably the most important thing.
As another example, I started training seriously last November with power and was doing my 2x20's @ 300ish. In 2-3 months I was doing them @ 320. This month I'm doing them @ 350-360. So that's 10 months of training and 50+ watts of gain. Sometimes it was two to three months of zero, and then quick jumps, but it happens if you're persistent.
VW
edited to add: I lost about 7kg too, and in the two to three months where I lost the bulk of that weight, my power numbers pretty much plateaued, though watts/kg continued to rise. Since May/June when I've held my weight steady, the numbers power numbers started going up again.