Light armor takes ages to level up in the normal way, but I have found a trick to it that will let you level up light armor without even having to be at you computer/console.
You will have to put the difficulty on the lowest possible level. You will also need some pretty sturdy light armor that can take a heavy beating and reduce the incoming damage by so much that you could just stand there and do nothing. And that is exactly all you have to do. Find a group of enemies (sword or archers/magic is fine) and just stand there and tank the damage. You will have to make sure that you aren’t taking too much damage that you will eventually die. Then you can walk away from the game and do something else for a few hours, but make sure that you check after a few minutes that you aren’t going to die eventually. When you come back you should have level 100 heavy armor!
The trainer for heavy armor is Nazir of the Dark Brotherhood in the Dark Brotherhood Sanctuary. Remember that any gold you spend on training you can picpocket back from him so that you don’t pay any gold. You will want to make sure that you do not train for more than 2000 gold before you pickpocket it back because then the chance of you succesfully getting your gold back is near 0% if not 0%. The location of the dark brother hood is (although you have to murder someone and then go to a bed before you can actually go into the dark brother hood):