the weapons that light up

[Garlyle]

There are two sets of "Glowing" weapons.

The ones you're far more likely to see are Relics - they're class-specific weapons with a long quest chain attached. After you complete the relic, there's additional quests to undertake to upgrade the relics, which give them added power and cause them to start glowing various colours. Because the Relic itself is fairly easy to complete, very powerful, and its first upgrade is very easy to do, a huge number of players at level 50 will have their Relic, so you'll see these glows very commonly.

Most recently are the "upgraded" Primal weapons, which are extremely difficult to obtain (Four of them require some incredibly rare ingrediants to craft, which have only become available as of the patch a week ago; the other requires a super rare drop from a very challenging trial to upgrade from another weapon) - these also have an elemental glow to match the weapon in question.