Smithing in this game is dumb as hell. I'm around level 29 now and my smithing is still really low so I can't do much with it when it comes to weapons and armour. How are you even supposed to level it up?
You level up smithing more by making things that are more valuable. You weigh up the raw materials you have, and maximize the value of the items you make.
So if you have 5 ingots, and you had the choice of making 5 items of 50gp each, or one item of 200gp, you make the 5 items for a total value of 250gp, this will boost your smithing level most..
Without gaming the system, the best way I think is to collect gold and silver, plus the jewels you find in chests and urns, and make jewellery items which have the highest value.
Boost your smithing perks so you can make and upgrade more valuable weapons. Get the Dwarven armor perk, go to a Dwemer ruin and collect lots of scrap Dwemer metal, smelt it into ingots and make lots of Dwarven armor and weapons, then upgrade them using the grindstone and the workbench.