I noticed that problem with weight increasing after an item's identified after the 1.3 patch, and there was no indication in the 1.40+ patches of any fix.
That also applies to the battlefield quests. Like you, I bring the items to the merchant questgivers, who thank me; sometimes I get the experience, sometimes I get nothing. The quest remains in my log. If I drop the item, the quest is noted once more as new in my log, and the questgiver asks whether I've done what he/she wanted, yet.
Next patch, perhaps?