I have been thinking about how that sort of mechanic might be applied to an OD&D game, since in OD&D fighting-men do not have skill points to assign to their weapons.
One possibility is to increase a particular weapon's power, based on the number of levels that the character is in possession of that sword.
For example, the character finds Blackrazor at first level. It is a +1 sword. As long as he continues to possess and use that sword, it increases in power, or extra damage, at certain intervals. The Game Table post suggested the following power scale:
1 skill point = +1
3 skill points = +2
6 skill points = +3
10 skill points = +4
15 skill points = +5
21 skill points = +6
Rather than tying this to skill points, you might instead tie this to the number of levels. The required number of skill points would, instead, be the current level of the fighting-man. So, if the character found Blackrazor, at first level, when the fighting-man reached 3rd level, the Blackrazor would a +2 sword. At 6th level, it would be a +3 sword. At 10th, +4, and so on.
I'm not sure this completely solves the problem, but I think it is a solution worth looking at.