You can also think of it in the sense that your item is say level 120. Normally if you leveled from 99 to 120 (excluding cap) without skilling, you would have a difference of 188 skill. I don't know the exact levels on these new weapons, but I expect it to be around the 115-120 range.
The reason the skill applies to weapon only, is because it is an ITEM level, not a job level. Since the skill will be applied to bayld gear too, we'll use that. So you get the nifty +188 axe and the bayld axe with +49. Your nifty axe is going to be lvl~120 so you get 188, but your bayld axe is only lvl~105 (49 skill levels difference). You don't get 237 skill, you get 188 skill and associated accuracy/attack bonuses in your main hand (logically you put the stronger in your main hand) and 49 skill with associated accuracy/attack bonuses in your off hand.
Edit: In response to what Mokiel said about how parrying skill plays into this, it re-enforces my theory in that your defensive skills are equally suffering when compared to your offensive skills when you look at difference of levels, hence why parrying is included. As to why Evasion is not included, because that is more something you do with your body, not your weapon. We may see evasion skill added to gear in a similar fashion.

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