How Bowen manages his weapons. (As of 0.9.6)

Bowen prefers dual wielding bladed weapons for melee.  So he will always try to keep two such weapons in his inventory while selling the rest. 

When a sword or dagger is added to his inventory they are placed on a "no sell" list, preventing Bowen from selling them to the first merchant he sees.  This remains until he equips any such weapon, then this list is cleared allowing Bowen to sell less effective weapons.

When a weapon is equipped, it is added to another list to track which weapons in his inventory he has equipped which also serves as a 'no sell' list.  If this list exceeds 2 items, the first item on the list is removed.  This is how Bowen keeps track of which weapons are his best.  The logic being the most recent weapons added to this list are the ones the game has decided are the most effective.  

Ranged weapons are handled in the same way except that Bowen only keeps one in his inventory.  

If Bowen ever has less than 2 swords/daggers or no ranged weapons, he will loot or purchase them until he has enough.  He will stop looking for new weapons if his basic needs are met.  So if you want him to have something superior to what he is using you will need to give it to him.  

Bowen will never sell The Huntsman if you have it installed.  In fact, he also will never sell it if you don't!