It seems to force you to keep looking for a replacement weapon - for AR, LMG and shotguns this is fairly easy, but I've not been finding many bolt action sniper rifles, and since you get just shy of 5k per headshot it doens't take long to max their individual xp bars.
On a side note weapons don't appear to gain any xp from fighting during arkfalls - I've been scoring over 1million damage on the leaderboards yet individual weapon progress doesn't appear to have budged. If they were working then that would max any weapon I've seen in one arkfall.