I'm not going to bother reading all the replies, and maybe my advice is late. If so, simply ignore it;
This is a common thing I do with my campaigns. I usually allow each character to have one "Heirloom item", which can have been given them by a family member, a teacher/mentor, a weird old man in a curiosity shop, or maybe they just found it, or maybe they made it, or whatever they want. This item levels up with them. However, I found that simply leveling up to the next bonus isn't quite as fun. It's not satisfying to have this item that's so very important to you and which means so much, then have it be no more powerful than any item you could get through Create Magic Item.
What I do is I take it's nature and expand upon it a little. If what they have is a weapon, then I also give that particular weapon a property no other weapon of that type has, such as 'brutal 1' on a spear. Half-way between that item getting each additional enhancement modifier, I try to give it something else. Nothing way super-great, but something that makes it notably better in a way beyond simple attack and damage bonus and whatever cool property it began with (flaming, for example).
By tenth level I come up with a way for the item to always be with it's owner, whether it instantly teleports into the scabard if it falls from their hand, or if they can will it into their hand, or if it flies back to them, or whatever. It offers zero mechanical bonuses (all magical thrown items are returning anyway), but it's cool and offers some interesting improvised uses to the clever player.
Weapons offer the easiest extra effects or abilities (new weapon qualities weapons of that type normally lack, expanded crit range, increased damage die, "bleeding" damage), and then you can do effects otherwise useful but not necessarily offensive (minor scrying abilities, minor healing or regenerating ability, increased speed... you're only limited by your imagination).
The problem is, don't do too much to make the weapon superly-mega-badass. If you make it brutal, increase it's crit range, and increase it's damage die, it suddenly becomes a MUCH better weapon, all around. I'd suggest one or two abilities that increase damage output. Brutal isn't too bad, as it only increases minimum damage, but something that increases maximum damage output is dangerous if you go overboard.
At any rate, simply leveling up alongside the owner, while cool, isn't quite cool enough, in my mildly humble opinion.