The weight of the arrow depends on the material used to make it.
First let’s understand that you pick an arrow based on the weight of the bow (poundage) and the archer’s draw length. That will give the spine (group) of the arrow you should be using.
There are ways to play with spine... longer arrows, heavier points, etc but let’s forget this for now and just follow the recipe.
You will find some aluminium arrows have a similar GPI (grains per inch). As soon as you move to the more specialised top of the line arrows they move from aluminium to carbon and then from carbon to some crazy alloy and the GPI changes significantly.
If you pick the right arrow with the right spine for the right length arrows will vary in weight based on the material they’re made.
Then weight play another part of the game.
Lighter arrows has less drop as you said but are more susceptible to wind and also more fragile. You shoot a few light arrows on a tree and they start to split.
Hunting ones are heavier as they need to hold more energy for penetration. Also it’s unlikely hunters will be shooting further than 30-40 meters/yards so distance is not the point of those kind of arrows.
Olympic archers will be looking for mid ground where arrows are not too light to be influenced by wind in those 70 meter shoots but also not too heavy to avoid the extra drop.
I have a feeling that as much as I added info RE arrow weights and materials I didn’t actually answer your question.
The lightest arrow practical for target shooting will be as light as the material that the arrow is made of allows but strong enough to be shot by a bow of certain poundage.
Given a certain bow with X pounds and an archer with Y draw length what's the lightest arrows we can use? Taken that James are not going to hide in this garage and make his Jame's special super light alloy to make his arrows we only have wooden, aluminium and carbon arrows available. We know that carbon is lighter (in general) so it needs to be carbon. So the lightest arrow you can shoot from your bow (safely) will be the weakest spine you can find for your bow and archer.