--- Which version to choose?
There are 20, 40, 60, 80 or 100 bow damage versions. Everything else it is the same.
The default follower's bow damage, unchanged by this mod is 7.
The arrow's damage is increased from 8 to 24, but in my latest playthrough, my follower never spawned them automatically, I had to add through the console. So you may need to provide arrows for your follower anyway. If you experience something else, I may make the "magic arrow's" damage to increase gradually as well.

--- How to install?
Remove old version (if any) by reversing what's bellow or using your manager.
Copy your choosen bow damage version into Skyrim's Data folder and enable in launcher.
- If you choose a low damage version, and later want higher damage, remove the old one and replace with the new one. No clean save needed.

--- What this mod does?
This modifies only certain values of that special version of the Hunting Bow, which spawns or respawns in your followers inventory in certain conditions.
The normal Hunting Bow is not changed. If you ever see in you followers inventory Hunting Bow and Hunting Bow - the easiest way to tell them apart is to check their weight: only follower version has a weight of 0 (set by this mod).
Special care was taken to avoid changing too much, as that may lead to incompatibilites with something - so name, ID and so on, remains unchanged. Any mod targeting the original, will succeed with this one too (for example those scripts which remove this from followers inventory)
This mod changes only:
- bow's damage from default 7 to 20, 40, 60, 80 or 100 (depending on what versions you choose to enable),
- the bow's model and related values, to look and act like the Imperial Bow - which is wooden and fits with most outfits
- weight from 8 to 0, so if multiple items of this type spawn, no weight related problems should occur
+
also replaces the auto spawning "magic arrows", made to look as the daedric model, as this seemed to be the most neutral looking:
- arrow's damage from 8 to 24
- quiver and arrow model and projectile same as the daedric
- quiver weight from 7 to 0

--- What's the purpose of this mod?
This can solve the annoyance of the low level bow spawning and switching, as now they will spawn and use this bow - without any performance impact, as no script is needed to run to check and remove the bow and do whatever else.
I still recommend to get mods which allow you to choose and decide your follower's fighting style, preferred weapon, inventory and so on (see below some recommendations). If you want your follower to become an archer, it's not enought to just give them a bow - as they will switch to their preferred weapon as soon as they can loot such a weapon.
If you don't mind, it's the best choice to give them both ranged and melee weapons, so they can switch between those - but specify which one to prefer.

--- Compatibility:
This should be compatibile with any mod - if any mod changes these values, the one placed lower in the loading order will win, but no problems should occur.
Mod created with Skyrim v1.6.89.0 - should work with previous game versions too, but I cannot test that.

--- Performance:
This can't affect performance at all, it's just the replacements of some values, only default models used.

--- Testing:
For testing, you can add it manually through the console:
press ~ then click through the console on your follower and type
inv
then press enter - you will see a list of his/her inventory (after adding check again)
then add the bow:
additem 10e2dd 1
then add 100 arrows or any number you want:
additem 10e2de 100
Then remove all other weapons (or use equip command instead additem)

--- These are not required - just follower related mod recommendations:

To change a follower's specialization, for example from two-handed into archer I recommend using Extensible Follower Framework - or any other you prefer, but this is what I like:
http://skyrim.nexusmods.com/mods/12933
and set specialization to archer,
and to give the follower a time to relax, use this instead (put in load order bellow EFF)
http://www.skyrim.nexusmods.com/mods/9504

The female follower from the pictures is Ria, you can found her here:
http://skyrim.nexusmods.com/mods/17354
There is a work in progress to improve her more here:
http://www.skyrim.nexusmods.com/mods/19983

I don't use horses, to much bugs, but if you want to try it, Convenient Horses is a very good mod and complements the above:
http://skyrim.nexusmods.com/mods/14950

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Credits:
Thanks to Bethesda Game Studios for Skyrim