Maybe you could put them into categories. Each category has an icon at the bottom of the screen and a corresponding key (number keys, I suppose).
Pressing the key cycles through the items in that category. You could have an inventory that way, with potions or scrolls etc.
You could also limit the number of weapons for each category and force the player to decide which to keep and which to throw away.
Categories could be:
Small melee weapons (daggers, short swords, hand axes)
Large melee weapons (long swords, battle axes)
Ranged weapons (bows, crossbows, slingshots, throwing stars)
Shields (only useable with one-handed weapons)
Spells (maybe two categories, offensive and defensive)
Items (potions, scrolls, stuff)