What reasons would a Bosmer Hunter have for wearing heavy armor? (This is for RP purposes. I like the look of HA over LA, but I can't think of any reasons why such a thing would happen)

He want's to be a ranged tank?

Maybe your Bosmer likes the look of HA.

Maybe he feels a lot more secure in big hard armor than soft paper thin light armor.

He knows he can be stealthy in any armor he chooses.

or

He wants to be ready for any situation, and knows that at some point stealth may not be an option.

or

Long range tank!

hmmm. D'oh! I forgot about backstory. Thanks guys

Aiming bow is easier when your enemy is standing right in front of you.

My knight uses heavy armor and she is quite proficient in Archery as well....so............yeah, its fine.

I actually find using heavy armor on an archer better than light armor because you don't get the perk ranger til 60 archery that makes you move faster with your bow drawn. Too often I'll be lining up my shots but i move so slowly i get hit often from other archers and meleers. Heavy armor helps with this.

Simply for protection.
Also - maybe your bosmer likes the look.

Regardless - if you manage your skills and perks correctly, there's no need to worry about heavy armor. My third character can sneak right up to falmer wearing a full set of ebony and carrying a daedric battle axe. So far, the falmer haven't reacted to the armor, but they always have a reaction when they encounter the axe................