The Red Sonja Method
In one of the Red Sonja novels, she claimed that she had killed so many magical beasts with her sword that it had become a powerful magical weapon, in its own right. Maybe you could do something like that?
If a non-spellcaster uses the same masterwork weapon for three levels/plus, and slays a number of magical beasts, magical humanoids, elementals, and/or outsiders, it becomes a +(character level/3) weapon (or double weapon).
So a fighter begins with a sword, uses it to advance through most of first level, and finally gains enough to purchase a MW (masterwork) sword. We cut him some slack, and let first level count... He rises to third, and his sword suddenly becomes +1. (Need to determine how many magical creatures it has to be used to help kill... 1/level? This will be hard, at lower levels!)
If he keeps the same sword to sixth level, it will become +2. At ninth level (provided he has slain the appropriate number of magical critters) it will rise to +3.
If you want to make it harder, restrict the types of critters, raise the number required (1/level at first, two at second, three at third), etc. Also note that, if he loses the weapon, or trades it in for another, his levels start counting all over, again! Thus, a fifth level fighter who loses his +1 sword will have to buy a new MW one (non-MW isn't enchantable), and will be seventh level before it becomes +1!... Of course, by then, he will probably have found better ones in dead foes' treasures!
Oh well, just an idea. With this, no magic weapons at first level (you can't afford the 300 GP for MW), and most characters will be fourth level before they can do anything with it.
Also, I would apply this ONLY to Barbarians, Fighters, and MAYBE Monks & Rogues. No Bards, Druids, Clerics, Paladins, Rangers, Sorcerers, nor Wizards. Spellslingers and Semi-Spellcasters can take the Feats and enchant their own (well, maybe Druids, Paladins, & Rangers can't - maybe let them).
Maybe all such weapons should be aligned to their "creator's" alignment, too, and gain one point of Intelligence/level... That might be cool (but maybe too powerful... although it would cut down on the picking up of dead PCs' weapons)!
I leave it to the DMs to decide whether or not Paladins can create Holy swords, or Rangers Arrows of Favored Enemy Slaying. (What would Druids make, anyway? Something that slays the "Extreme" alignments (CE, CG, LE, LG)?)
The idea probably needs some research and work...
(PS: Note that the PCs (except, perhaps, the Bard!) need not be AWARE of the requirements for advancing an item, either! You just inform them when an item gains a plus! ;-p)
