Obviously at the bottom we have slaves. At the top some sort of royal heirarchy. Our cities are going to be mostly underground and this is strange for a group of people who find such beauty and reverence for light.
The answer, I propose, to dealing with this is that light was a gift. A blessing, even, straight from the Gods. Those who were of higher social standing could walk among and bask in the ligh because they were selected by the Gods to be worthy of the light, but the farther down you go in the social structure, the less worthy you were. The Ayleids built their cities underground so that they wouldnt offend the Gods.
this doesnt mean that the Ayleids didnt venture out during the day or anything, on the contrary. Ayleids preferred to bait their opponents in war in the early hours of the day so that when battle came the sun was shining. Ayleids fought their battles during the day, hunted during the day all hoping to receive the blessing from the light. Ayleid peasants and simple soldiers believed they were twice as strong and fought more bravely whenever they fought in the sun or were bodyguards for their aristocrat masters when they roamed Nirn. This sense of strength turned to an arrogant pride, where the Alyleids felt undefeatable in the sun and stacked their defenses poorly and outnumbered.
Summary, Ayleids longed to spend their time in the sun and basked in it when they could. They didnt want to overstep their bounds however so they built their cities where the natural light could not reach as to not offend the Gods.