So possibly, at later levels it might take more skill-ups to reach a new level?
My understanding is that every time you gain a skill point, you gain some XP, which applies towards leveling up. The higher that skill is, the more XP. So let's just say your one handed skill goes from 20 to 21, you might get 21 XP. If it goes from 90 to 91, maybe you get 91 XP.
Levels require higher and higher XP, per level, and if you max everything out impletely it will take you into the mid 70s.
So there is no set amount of skill points per level, but it averages out around 20 per level. At lower levels, 5-10 will probably do it.