Likely this bug has been around as long as the item property has been, but I couldn't find anything on it when searching.
What happens, is that each time the character throws an axe with the 20% of base item weight property, the game removes 1 pound from the encumbrance even though the item only weighs 0.2 pounds. Over a stack of 50 the characters total weight carried is reduced, permanently, to 40 pounds lower than it is. Relogging seems to be the only fix.
I'll probably just make a second throwing axe entry in the baseitems.2da with the adjusted weight as a workaround, if that becomes essential, but simplest would be if there's a way to make the game recalculate the carried weight.
The Lexicon doesn't list a function to do so, GetWeight() seems to be the only encumbrance related function available. Is there a script of command that does this that I'm not aware of?