My character favorites ebony weapons, which I've already improved at the grindstone. I don't have any smithing perk and it's a long way to the ebony smithing perk, which would improve ebony weapons twice as much. Since I've already improved them once, will I have the chance to improve them further thanks to the perk or they can be improved only once?

yes you can smith them more than once. If you enchant them however, it is a once and done deal.

Only if he doesn`t get the improve magic Weapons and Armor perk.

Ah good to know, thanks.

as you develop the smithing skill you can improve any weapon or armour using the tables or grind stone - I've got as far as Epic and not sure if there's anything about that yet - you can also enchant the item, which means if you don't have the perk to "smith" magical items you can't improve them any more - I suggest that you spend at least take that one perk that way you can still improve enchanted items

Sorry for not being more clear on that. What I meant to say was, once enchanted, that weapon can not be re-enchanted to enhance the enchantment. you will be able to smith the weapon to increase the base damage, but the enchantment will remain (weak).

It goes up to Legendary at maxed out smithing.

I hav e 100 smithing, a smithing ring and necklace and I drink a smithing potion right before improvement. You can get really killer armor and weapons this way. I believe my dagger is rated at 92!

Yep. You can enchant a single weapon twice, with the last perk in the Enchanting tree. The strength of your initial enchantment relies on perks and soul gems, you can't constantly improve an enchantment on a weapon.