For all the modding I've done to the game, I've never touched arrow weight or any other way to limit them.
Reason is the game is already so unrealistic in how many arrows it takes to kill something, plus how many enemies you run into in a short time - and, well, you need all those arrows. And if you have to carry a few hundred arrows, then they should darn well be weightless.
"Unrealistic" in and of itself has never bothered me in these games. It's balance and the logic of the mechanic taken as a whole that does matter.
For example - if you want realistic damage and hits, then almost any landed blow is crippling. Only unarmed brawling makes sense with the hit point system. In real combat, doesn't matter how fatigued or armored I am, if an arrow connects - I am out of the fight bleeding to death unless I treat it.
Secondly, if you are wounded in battle, it takes a long time to heal. You fight one battle a month, not 15 per day.
So, once those basic realities are out the window, I'm just fine with weightless arrows.