It is possible to sell your unwanted equipment to the General Store ([Pierre's][1]) or any other NPC shop such as the Adventurer's Guild.

[This][2] page on the Wiki also gives you a buy/sell price for each weapon/type you want to sell.


  [1]: http://stardewvalley.wikia.com/wiki/Pierre's_General_Store
  [2]: http://stardewvalleywiki.com/Weapons