It began happening at level 5 (in fact, almost immediately after I achieved level 5), although I have played several characters previously (back in February/March), and I'm sure my skills didn't increase this fast. My character is now level 7, with all my combat/awareness and spell skills maxed or near to maxed.
It takes me about 20 seconds to gain the extra 10 skill points to max a skill when I level up. For instance, almost every time I cast "Soothe" (a low level Druid spell) I receive a point in Alteration. That makes it incredibly easy to max the skill as I don't need to engage an enemy. When I was level 5, I stood about 30 metres from a stealthed enemy for 40 - 50 seconds (petitioning because my skills were shooting up) and my detection and awareness skills maxed (reached 50) within that time. I then proceeded to complete the quest aware of every single stealthed enemy in the building, making it far too easy.
I sincerely hope this is a bug. If it is part of the default gameplay, skills might as well be removed and the benefits they bring directly tied to my level. Sorry for the whinging

but when I first started was very pleased to have skills that appeared to matter. I'd stop and think before attacking; my evocation skill is falling behind, I'll focus on that for a while. Now I just select a random enemy and get 5 - 8 skill points in the one fight. How it plays now reminds me of World of Warcraft's system where skills
are tied to your level (i.e. if you were level 5 and had a Hand-to-Hand skill of 0, that skill would increase at an incredibly accelerated rate if you used it until it hit the mid-40s). Besides, the GM seemed to think it was a bug...