Yes. I'm very wary of wasting arrows. Nothing infuriates me more than burrowing 4-5 arrows into a bear, running to the corpse, and not getting any back. I know there's a perk that gives you more back, but I haven't decided if it's worth it.
Anyway, I do agree that arrows should have weight. At 0.1 per arrow, 200 arrows would be 20 lbs, which is relatively fair compared to the weight of other weapons. You shouldn't have 1,000 arrows in your bags. When a quest giver or the quest log says 'get prepared before heading out', stocking up on enough arrows should be one of the things you need to do before going out on a long journey.