" These skills are raised just by using them on mobs of the appropriate level to your skill. "
In otherwords, if your skill cap is near a level 50 cap for that weapon of your current job, then killing level 51+ mobs would raise its skill. Assuming it is not capped already, as in displayed in blue.
Take this for example
- You're a level 68 Warrior and you want to skill up Great Axe which is currently at 175. You go to the chart, look up great axe, see that it is around level 55 that it caps to 178. So killing anything level 55+ would raise your Great Axe skills.
- Another example, you're a level 68 Warrior and also have a level 75 White Mage, and you want to skill up Club which is at 217. You won't be able to since it is capped for a level 68 Warrior at 217. However, for a 75 White Mage you can continue skilling up to 256.
- At 217 for White Mage you can kill anything level 68+ to skill up club at 217.
Popular mobs people like to kill for skilling up are crabs because they usually do defense boost.
- Look for the appropriate level to your skill for crabs to kill http://wiki.ffxiclopedia.org/wiki/Crab