Ok. Here's what you need to do:
1) Get
Smithing to 100.
2) Get/Make items that improve weapons/armor by a minimum of 20% e.g. Ring of Eminent Smithing, Glass Gauntlets of Eminent Smithing, etc.
These items can be combined, so say you had a necklace and ring that added up to over 20%, that's fine.3) Drink a Blacksmith's Elixir (you can buy or find these).
You now have a legendary item.
To improve items even further, if you get your
Enchanting to 100 then get Enchanter 5/5 and Insightful Enchanter you can then disenchant any item that improves Smithing to get the Fortify Smithing enchantment.
You can then create Necklaces, Rings, Armor and Guantlets that improve weapons/armor by 25% for each piece equipped by using a Black or Grand Soul Gem.
The more pieces you have equipped, the better the armor/weapon will be. Even when it says "Legendary" that doesn't mean it's the best. Using one item that improves smithing upgrades by 20% and a Blacksmith's Elixir gets you a Legendary item. Using 4 pieces of 25% and a Blacksmith's Elixir makes a much better Legendary item.
If you add Alchemy into the mix, you can create potions to improve alchemy and end up creating Blacksmith's Elixir's that give a 130% boost instead of the standard 50% and Enchantment Potions that allow you to create items that improve smithing upgrades by 29% instead of 25%... but I'll let you look into that if you want to

- I have not done it myself.
Oh, and no having a higher light armor skill makes no difference to item upgrades.