Dravean from over on the Adventures Dark and Deep Forum has an idea of slowly removing a penalty for not being proficient with a weapon so long as that weapon is actually used in combat for a length of time.
1. Each weapon the character has access to or is proficient with he has a base of -1 to use when he first switches to that weapon type.
2. Any character can use a weapon he is not familiar with at a penalty of around -3
3. After some time of using the weapon in combat the penalty is reduced by one and possibly allowed to go up to +1
4. Once a character reaches +0 with a weapon he is not familiar with he is now considered familiar with it.
5. If switching from one weapon to a new weapon he is familiar with but has not used in sometime then the penalty may fall back down as low as -1
I don't think I would actually wait until an adventure is done too adjust the penalty or bonus but maybe base it off of getting like 5 successful hits or maybe surviving 2-3 fights using the weapon. Maybe even base it off xp.
I believe this system would give players a feeling of personally earning specialty in weapon while still allowing and even encouraging some players to switch up their weapons. Since they can gain new familiarity or maybe even switch weapons daily to try and keep a higher level of familiarity. And at the same time making it too where finding a slightly better magic weapon isn't reason enough to just drop your old one.